THEY say stand-up is a craft to be learned and the stand-up circuit a slow slog to be endured.

But pop up in the right place at the right time, and the world of comedy is fast-moving enough for a sell-out Fringe run or a memorable telly slot to make a big name out of a little one overnight – or, in the case of 29-year-old Devon-born comedian Josh Widdicombe, over 10 consecutive nights and a Christmas Special. That was the number of times Widdicombe co-hosted The Last Leg With Adam Hills, a programme running daily on Channel 4 as an adjunct to and commentary on the network's coverage of the 2012 Summer Paralympics.

Originally intended as a one-off, it proved wildly popular with audiences and is currently on its second series. Now called simply The Last Leg, it's still presented by Sydney-born Hills, with sports journalist Alex Brooker acting as a second co-host alongside Widdicombe. And, it's fair to say, it's made Widdicombe considerably more recognisable than he was this time last year.

The format is simple. The trio throw insults at each other (and, occasionally, East 17) and comment on the week's news from an off-kilter perspective. Employing the now-infamous hashtag #isitok, they also field apparently unaskable questions tweeted by viewers. Such as "Is it OK to hit a disabled person if he's being a nob?" That one aired in the first series and generated plenty of controversy in the more easily offended section of the popular press. Adding a little bite to it all is the fact that both Hills and Brooker have prostheses: Hills was born with no right foot and Brooker, who also has hand and arm deformities, had his right leg amputated as a child.

It was in a Starbucks in London that Widdicombe was asked by the show's producer if he wanted to be involved. "I thought, 'Well, it's the week after Edinburgh and the worst case scenario is that I get to go to the Paralympics and nobody watches it. So why not?' You imagine these big decisions in your life being like forks in the road but this one was just, 'Why not?'. If I hadn't done it, I think my life would have been very different at the moment."

Widdicombe, who had recently being doing a sports slot for Channel 4 show Stand Up For The Week, knew Hills from the London comedy circuit and from the Edinburgh Fringe. Brooker he only met the day before the series started. Luckily, the three men clicked.

"We thought it was a late-night Paralympics round-up show so we weren't going in saying to each other, 'If this goes well, we could get a 9.30pm slot on a Friday night'," he laughs. "No-one could have imagined that. I think a lot of the success comes from the chemistry between the three of us and luck, to a certain extent. It just happened that we worked well together."

Helping them out over the course of the two series has been a stellar list of guests, including Paralympians and Olympians such as Jonnie Peacock and Christine Ohuruogu. Idris Elba, Jimmy Carr and Jonathan Ross have also featured. Moving beyond disability issues and the Paralympics for the second run has required a shift in focus, but one of the biggest news events of the current series has drawn them right back into both those subjects: the shooting in South Africa of Reeva Steenkamp by her boyfriend, Oscar Pistorius.

"We had a show the day after it had happened and there was a lot of discussion about it," says Widdicombe. "We didn't do jokes, but we addressed it. Adam is a brilliant host and one of the things he's very good at is feeling where the tone should be and what we should do, and what is right and what is wrong. You can't really buy his kind of judgment."

The Last Leg continues on Channel 4 until Friday, when the second series ends. There's no rest for Widdicombe, however, because on Monday he brings his wry observational humour to Glasgow for an appearance at the city's comedy festival. For connoisseurs of stand-up, his Scottish date will be hotly anticipated given his growing reputation on that front. A regular at the Fringe since 2008, when he made it to the final of Channel 4's So You Think You're Funny, he won the Best Newcomer accolade in the 2011 Edinburgh Comedy Awards, the successor to the Perrier. But has his newly acquired TV profile altered what audiences expect of his live show?

"I don't think so," he says. "I've yet to be heckled along those lines. The tour shows are really good unless I've totally misjudged it and half the audiences are going, 'What the hell is this? We want to hear another anecdote about Paralympic swimming'."

Born in Devon, also home to his beloved Plymouth Argyle, Widdicombe grew up in "a tiny village in the middle of nowhere on Dartmoor". It sounds quaint and pastoral and very far from the northern cities whose comedians still power the business. There isn't, I venture, much of a Devonian stand-up tradition to pitch against the working men's club scene so lovingly sent-up in Peter Kay's Phoenix Nights. "There isn't, is there?" he agrees. "There's Charlie Baker and there's me." He pauses, before remembering a third. "Dawn French. She's from Plymouth."

At school he had the kind of experience you expect most comedians do but which cliché tells you they don't. In other words, he went pretty unnoticed pretty much all of the time. "Most people I was at school with, if they saw me on telly, wouldn't know I'd been at school with them," is how he puts it. Not the class clown, then, though from an early age he had keen interest in television comedy. Fantasy Football League was his favourite – in particular Frank Skinner, "the funniest man in the world", who co-hosted with David Baddiel – but he also found time for Shooting Stars, Father Ted, The Royle Family and The Fast Show. "It was," he says, "an amazing time for comedy on TV, though not so much for stand-up, which I'd say is in its zenith now."

From school, he went to Manchester University to study linguistics, the city chosen because it was where The Smiths came from and because it wasn't in Devon. He watched some stand-up in Manchester – he recalls being wowed by a pre-fame Jimmy Carr – but it wasn't until he moved to London that he first dipped his toe into the world of open mic nights. Even then it was "desperation" that drove him, he says.

"Stand-up wasn't a calling. It was more like, 'What can I do that isn't going to make me really depressed?' I really struggled with doing nine-to-five and just wanted to do something where it felt like I was in charge and I was doing something creative. I imagine if the first gig had gone badly I'd never have done it again. I imagine there's hundreds of people who could have been really great comedians and just had a bad first gig. But I had a good first one and it kind of just snowballed."

As well as his regular slot on Stand Up For The Week and an appearance on Live At The Apollo, 2012 saw Widdicombe land his first appearance on a programme he had previously only written for – BBC Two's Mock The Week, the show that catapulted Frankie Boyle into the national consciousness. He's also been a feature of radio programmes like Arthur Smith's Balham Bash, on BBC Radio 4, and BBC Radio 5 Live's Saturday morning sports show Fighting Talk, currently hosted by Colin Murray. Now, courtesy of the Paralympics and one of the most unlikely TV hits of 2012, Josh Widdicombe finds himself moving onto a new level entirely. He won't confirm that a third series of The Last Leg has been commissioned but admits that it's looking positive.

"I remember turning to Alex at the end of the final episode of the first series," he muses, "and saying, 'Be aware: we will never be involved in anything as successful as this ever again.' And I kind of stand by that."

So is it OK to think we haven't seen the last of him, or it, just yet?

Josh Widdicombe: The Further Adventures Of- is at The Stand Comedy Club, Glasgow, on March 18 at 9.30pm, as part of the Glasgow Comedy Festival. For more details: www.glasgowcomedyfestival.com