In the middle of the British Library, trillions of words stacked up on the shelves around her, the novelist and poet Kate Clanchy is struggling with one word in particular: Scottish.

What does it mean? By any definition, Clanchy is Scottish. She was born in Glasgow and raised in Edinburgh, her parents are Scottish, and yet, perhaps because she was educated at Oxford University and has a gentle accent that is sometimes mistaken for English, she has often been labelled as Not Scottish or, even worse, Not Scottish Enough.

It's a problem of identity Clanchy has faced her whole life and one that's had some serious consequences for her career. It is also, among other things, what her engaging new novel, Meeting The English, is all about. The plot follows a Scottish teenager, Struan Robertson, who goes to London to work as a carer for a novelist in Hampstead, but all the way through certain questions recur. What is nationality? What is English? What is Scottish? And does any of it matter?

In the British Library cafe, surrounded by bibliophiles focused on their carrot cakes and laptops, Clanchy turns her coffee cup round and round and explains how these questions have affected her and some of the startling answers she has to them. She was bullied at school, she says, because others thought she was English. Then she couldn't get a job as a teacher in Scotland because she trained in England. Later, when she won the Saltire Society First Book of the Year Award for her poetry collection, Slattern (1996), she says there was whispering about her eligibility, with one literary magazine openly questioning her Scottishness. It has left her feeling jaded and frustrated about what it's like to be English – or to be seen to be English – in Scotland.

"It's a problem if you're in Scotland to be English," she says. "People are prejudiced even if you're a tiny bit different." She gestures at the people round her, then talks about the streets outside and all the nationalities that are out there. That's what London is like, she says, but in large parts of Scotland, even these days, it still isn't and it certainly wasn't in 1989, when Meeting The English is set. In an early part of the book, Struan, who is from the fictional town of Cuik, marvels at the number of foreigners on the Underground: "Were they tourists? ... he flushed scarlet with the strangeness of it." By the end of the book, he's grown up and met a whole new range of people. In particular, he has met the English and discovered they're the same as the Scottish.

"The difference between English and Scottish is surely a small enough difference for us to get over," says Clanchy. "And to think that was the difference that dominated my childhood. Now when I look at my children aged eight and nine, going off to their multicultural schools, the difference between them and their classmates is not the major thing. If someone was Scottish in their school, it wouldn't even register."

The school the children go to is in Oxford, where Clanchy also teaches creative writing one day a week, and it's interesting to contrast that with the experiences of Mr Fox, the teacher in Meeting The English, and what happened to Clanchy herself when she tried to teach in Scotland. In the book, Mr Fox is bullied by the pupils at Cuik High School; by contrast, Struan is welcomed in London. It's part of a feeling Clanchy has that the Scots have always been more welcome in England than the English have been in Scotland.

"There was always this thing that I couldn't get a job in Scotland," she says. "I remember being surprised when I got the Saltire Award because I thought 'I'm not allowed to work as a teacher therefore I'm not Scottish but you want me to be a Scottish writer?' I'd stopped thinking of myself as being entitled to be Scottish. I couldn't register with the General Teaching Council for Scotland. It's powerful to say: 'you've been to England therefore you're not entitled to teach our children'." I ask her if that felt like anti-English prejudice and she gets irritable for the one and only time in our interview. "Well, it is, isn't it?" she says. "Because someone who comes with a Scottish qualification can interview in England and get jobs in England."

She believes all of this has serious political consequences – in particular she thinks an obsession with being Scottish means we ignore the real differences between people. "One of the things that worries me about the independence debate is that it stops people from acknowledging the class differences. That thing of 'we're all socialist in Scotland and we're all terribly equal'. It's not true. Edinburgh has a Hindu caste system; I've never seen anything like it. There's the lawyers and the doctors and the civil servants, generation after generation. It's extraordinary."

The best way to describe how she feels now about her nationality, says Clanchy, is ambiguous and here perhaps you can feel the influence of her memoir Antigona And Me (2009), in which she described how she came to employ and then befriend a Kosovan refugee (they are still friends now). "I'm with people all the time who have no difficulty being Tanzanian-British or Bangladeshi-British," says Clanchy, "so why is it difficult to be Scottish-British? It's what I feel."

In Meeting The English, Struan feels something similar. He stands in front of the mirror and realises he has become a mix of things ("he could see Scottish Struan under the English tan"), partly because he's found self- confidence from having to care for Phillip Prys, the loud, alpha playwright and novelist silenced by a stroke. Prys doesn't say a word in the entire book but in some ways he's the most striking character. There he is in a wheelchair, helpless and silent ("the words accumulating like pee in the bag"), a symbol of all the bigger events of 1989: the Berlin Wall gone, Thatcher going. "Thatcher's not even mentioned but she's in the background," says Clanchy. "Suddenly, all the old tyrants are dead so what are we going to do?"

There may have been another, perhaps subconscious, reason for Clanchy to choose 1989: it was before mobile phones. Sitting as we are next to a wall of books, we talk for a few minutes about the consequences of the mobile for the novel. Could the fact that characters can just text each other destroy plotting? Clanchy thinks not, although she is not a fan of digital technology. Reader comments on the internet, for example, she describes as "a masked ball of abuse" where everyone has a mask except you, and she is not keen on blogs either.

"It feels like I haven't got enough words to do all that. I couldn't ramble something off, it would do my head in. I can only do 500 words a day and that includes email." She likes getting things right, she says. And how does she know when that is, I ask? She looks up at the wall of books. She turns the cup round in her hand. Then round again. It's when all the words are jammed up, she says. Like a dry stone wall. All the bits balanced on each other. Perfect. Just right.

Meeting The English is published by Picador, priced £16.99

It's a problem to be English in Scotland, says Kate Clanchy