When I arrive at his north London home, Nick Robinson is out. He’s running late, apparently, so daughter Alice shows me through to the kitchen and makes me a cup of tea. Alice, 20, a student at Oxford, is on a flying visit to London before heading to Edinburgh, where her university a cappella group Alternotives is singing at the Fringe. She’s excited and nervous at the prospect.

Later, the BBC’s outgoing political editor tells me Alice’s Edinburgh jaunt will be a nice “rounding off”, since it will mark exactly 21 years since his wife Pippa discovered she was pregnant with their eldest child, while the pair were queuing to see a Fringe play. The couple are preparing to travel to the city again, for Robinson’s appearance at the Book Festival – and, of course, to see their daughter perform. “To think that baby is now going to be singing in the Fringe is rather lovely,” beams the proud dad.

It transpires Robinson, who also has two sons, aged 14 and 18, is late because he has been receiving his final round of chemotherapy – a precaution – for the lung cancer that has largely kept him off our screens for the last few months.

A self-confessed workaholic, he’s been doing what is arguably the most high-profile job in UK journalism for the last decade, but will move on to present Radio 4’s Today programme later this year. Scot Laura Kuenssberg was recently announced as his replacement, the first woman to do the job.

Joining me at the table in the family’s small basement kitchen overlooking the back garden, Robinson, 51, looks and sounds well, and sheepishly apologises for the stubble he’s allowed himself to grow since taking time off to recover.

The voice he lost completely following surgery to remove the bronchial carcinoid tumour back in March sounds a bit husky, and tires after a while, but it is back. And it is unmistakably Robinson.

In his recent book, Election Notebook, he admits the very real prospect of not regaining that voice was worse than being told he had cancer. “It’s who I am,” he writes. “Without words, spoken words, I am nothing.”

The book, written in diary form, is a fascinating and thoroughly engaging behind-the-scenes look at how political campaigns are won and lost, and the part journalists play in the narratives. He says he wanted to “pull the curtain back a bit”, to give voters who aren’t necessarily passionate about politics an insight into how the game between politicians and journalists is played.

Covering the period leading up to last year’s independence referendum and on to May’s general election, it also ends up being a moving and sometimes blackly humorous account of Robinson’s cancer diagnosis, the surgery that followed and his not entirely successful struggle to regain his speech in time to cover the election. The book tells how he was in his pyjamas just an hour before nervously appearing alongside David Dimbleby to reveal the exit poll on May 7. Would his voice hold up? It did.

This wasn’t the book Macclesfield-born Robinson intended to write, of course, and he seems cheerfully bemused by the inevitable media focus on his health. Tellingly, however, the cancer narrative gives the book an extra and sometimes surreal dose of humanity, which works particularly well when set against the all-consuming - but often fatuous - cut and thrust of party politics. It is written in the same wry, quick-fire, accessible style that has made him a mainstay on the nation’s screens.

In person, Robinson is down-to-earth, open and funny, generous with anecdotes about politics, his treatment, a recent holiday with Pippa – a relationship counsellor who he met at university – in Suffolk. More than once he prefixes a horrible cancer experience with “I can laugh about it now”, and you get the impression the stoicism that comes across in the book isn’t put on.

Scottish readers of the Election Notebook will, of course, be particularly interested in the sections about the referendum and the now infamous row with Alex Salmond that made headlines a week before the vote. The fact that the broadcaster’s appearance this week at the Edinburgh International Book festival is sold out is quite possibly more to do with the spat and its consequences than the tome itself.

Let’s go back to that day. The former first minister was giving an international news conference in Edinburgh on the day RBS confirmed it would move its headquarters to London if Scotland voted for independence. A number of other high-profile businesses had come out against a Yes vote.

At the press conference, during a long and bad-tempered exchange, Robinson asked Salmond two questions, one on RBS specifically, the other on why voters should believe SNP assurances over big business warnings.

Salmond answered the second by accusing Prime Minister David Cameron of lobbying businesses, before moving on to attack BBC reporting of “market sensitive data” that he said should not have been released by the Treasury. Salmond moved on but Robinson continued to ask questions off-mic, leading the former first minister to accuse the BBC journalist of “heckling”.

Robinson’s report for BBC News featured an edited version of the exchange, and a voiceover that claimed Salmond “didn’t answer” the second question. It was a phrase that would come back to haunt him.

The entire exchange immediately went viral on social media, leading to thousands of complaints to the BBC from pro-independence supporters about Robinson’s reporting. In the minds of some in the Yes movement, the incident crystalised what they viewed as the BBC’s biased coverage of the referendum. Demonstrations were held outside the corporation’s Glasgow headquarters, with protestors calling Robinson a liar and calling for his resignation.

Salmond himself accused the corporation of “unconscious bias”, telling The Herald just before the vote: “I think the metropolitan BBC has found this thing extraordinarily difficult, to separate their own view of the world from their view reporting Scotland."

No journalist wants to become the story. So, how does Robinson view the exchange now?

“There’s no doubt at all that the phrasing of that report wasn’t clever,” he says. “I did agonise about how to boil down this piece. My Q&A with Alex Salmond lasted seven minutes, my report lasted three and a half. In that three and a half I had to get the views of the various businesses criticising independence, the No campaign, as well as my questions and the answers. In the end that’s what I’m paid to do, and it’s not an excuse, but it is an explanation – trying to capture all that was being said was very difficult.”

He expands further. “The phrase ‘he didn’t answer’ was clearly open to the interpretation that I meant he didn’t say anything, which is absurd, and it never occurred to me that people would see it that way. But I wrote the phrase and it wasn’t good.

“What I was trying to point out to the viewer was that [Salmond] chose largely not to address the points I put to him, and to have instead an argument about something else.

“God, I wish I could write the phrase again.”

Robinson reckons Salmond was spoiling for a fight and needed a distraction on a day when the headlines were not going his way. In the book, he accuses the former first minister of “an utterly calculated attempt to put pressure on the week before the referendum”.

To prove his point, Robinson reads me texts sent by one of Salmond’s advisors after he had apologised for the phrasing of his report.

One says: “It was a good couple of questions, you got a good answer. You’re an old hand at this and know the score.”

Another says: “We were upset about the package. Alex and my team regard you as a fair and professional journalist.”

Robinson chuckles wryly. “Try telling that to some of the people carrying banners saying you’re a liar and should be sacked.”

He says he detects a change of approach from new first minister Nicola Sturgeon, throwing in that he will be meeting her, informally, while he’s in Edinburgh. She was one of the first politicians to tweet support when his illness was made public.

The referendum is clearly still at the forefront of Robinson’s mind. He describes it as “within the top two” most exciting stories he has ever covered, and says his abiding memory of the campaign is of “the most exciting, exhilarating time”.

The personal nature of the criticism clearly rattled him, though he says the row itself didn’t come as a big surprise.

The BBC cleared Robinson of any wrongdoing in relation to the Salmond report, but accusations of bias continue to be made by sections of the pro-independence movement. Among the critics is Herald columnist Iain Macwhirter, who has written widely on the ignorance of the “metropolitan media” with regards to Scottish politics.

I ask Robinson about the recent Audience Council Scotland report that criticised the tone of the BBC’s coverage, pointing to an “Anglified perspective”. I posit that even if there wasn’t institutional bias, the perception that the BBC was not impartial raises serious questions for the corporation.

He agrees that it is right to “reflect and debate”, but defends his own and the BBC’s handling of the coverage.

“I want to say, very firmly, that the way I tell a story should not be dictated by an opinion poll or a focus group, or the latest call I get from this or that political party,” he explains. “That isn’t journalism, that’s followership. That isn’t what I’m paid to do. I’m paid to find out what the story is, and report it.

“What I’m very struck by is that people often generalise that there is a bias, and that comes from both directions - we got as many complaints from the Better Together campaign.

“It is perfectly proper to have a debate that says, ‘do I want some guy from London coming up to cover Scottish politics?’. On one level, the referendum was a decision for those who live in Scotland.

“On the other hand, this was a decision with a huge consequence for the whole of the UK, and the licence fee is paid by people from throughout the UK, and it was right that the political editor, the economics editor, the business editor, should all go to cover the most important story of the year, if not for many years, and should report on it in the way they would report on any other story.”

Robinson describes accusations that he reheated old allegations and simply doesn’t get Scottish politics as “absolute nonsense”, saying his job as political editor brings a responsibility to ask the big questions.

He also refutes that media coverage of the referendum had a direct impact on the outcome. “Why the referendum was lost [by the Yes campaign] was because, as in any choice around change, those who were advocating change were not able reassure people that it was a risk worth taking,” he says. “Fear wasn’t created by ‘metropolitan journalists’ coming up to Scotland. The fear had been there for decades.”

Another referendum is “likely” he suggests, though he argues the possibility presents a complex “risk calculation” for Ms Sturgeon.

After 45 minutes of full-on discussion, Robinson’s voice is starting to tire. We move upstairs to the sitting room where the photographer has set up his equipment. The hallways of the three-storey property - the sort of classic north London terraced house that 20 years ago would have been lived in by teachers or civil servants, but in the current market wouldn't give you much change out of two million – are covered in photographs of the Robinson children and their parents through the years.

The sitting room is a welcoming, lived-in space, packed with books and records, and an upright piano takes pride of place. The records range from classical box-sets - “my grandfather’s” - to Stevie Wonder, while the bookshelves are overflowing with political biographies, fiction and an impressive collection of vintage Asterix books that Robinson has collected since childhood.

He hopes to make a full recovery from the cancer – his type of tumour has a good prognosis - and laughs when I ask whether illness has changed his relationship with his work. “It’ll be interesting to see,” he says. “I’m a self-confessed workaholic, so in a sense it was an unplanned treatment for workaholism. I don’t want to sound like a cliche, but of course it gives you a bit more perspective. I’ve had lots of enforced rest. For me to miss covering a general election is like missing a World Cup if you’re a football correspondent – it’s a big deal. But I quite quickly found it is not the most important thing in the world – your health is.”

Robinson is a huge football fan and a lifelong Manchester United supporter. His next project is a BBC documentary on the leadership qualities of the man he described as the “greatest living Briton”, Sir Alex Ferguson, to be broadcast this autumn.

Around the same time, all being well healthwise, he will take over presenting duties on the Today Programme from Scot James Naughtie, who has been in the job for 21 years.

The journalist says he’s not looking forward to getting up at 3am, but is excited about “breaking free from the narrowish confines of party politics”.

“My old mentor [late Today presenter] Brian Redhead used to describe the job as ‘dropping a word in the nation’s ear’,” he says. “There’s something nice about being at the beginning of someone’s news day.”

In 1982, Robinson survived the car crash in France that killed Redhead's son, Will, his best friend, and another good friend, James Nelson. Robinson was lucky to escape with his life and spent weeks in hospital.

He is full of praise for Naughtie, who he describes as a “giant”.

“I can’t be a replacement for Jim, I’ve got to be me,” he says. “Hopefully I’ll bring my own style and interests. I’ve discovered I’m the only presenter who’s into football, so you might get a bit more of that.”

Robinson says his successor as political editor, Laura Kuenssberg, the youngest ever incumbent of the job in a list that also includes Andrew Marr and John Cole, is “incredibly impressive”.

“When she says MPs are saying something or other, Laura will have spoken to 20,” he explains. “I think she is the journalist with the most MPs following her Twitter feed. She’ll bring a real commitment to digging out stories and a real passion for and belief in politics. The great privilege of the job is that you get the chance to shape the national conversation on politics.”

A slightly wicked smile crosses Nick Robinson’s face when I mention Keunssberg’s Glaswegian roots.

“I’ll make a wee prediction for you,” he laughs. “The fact that she is from Glasgow and a Scot will not protect her from the sort of rows I got involved in.”

Nick Robinson will be appearing at the Edinburgh International Book Festival on August 20. The event is sold out. Election Notebook is published by Bantam Press, priced £20.

CV

Name: Nicholas Anthony Robinson

Age: 51

Born: Macclesfield, Cheshire

Family: Married to Pippa, a counsellor, three children aged 14, 18 and 20.

Education: Studied Politics, Philosophy and Economics at University College, Oxford. President of the Oxford University Conservative Association.

Career: First job in broadcasting was at Piccadilly Radio in Manchester. Joined the BBC as a trainee in 1986, then worked as a producer on Newsround and Crimewatch. Later worked on Panorama.

Became a political correspondent in 1996, then chief political correspondent for the BBC News Channel in 1999.

In 2002, left the BBC to become ITV’s political editor, a post held for three years.

Returned to the BBC as political editor in 2005, taking over from Andrew Marr.

He has held the post for a decade, but moving to present the Today programme on Radio 4.