When Small Island was published five years ago it started out faring much the same as Andrea Levy's first three books: well reviewed but not particularly widely read. "Give me a basket and I'll go door to door with it," she joked to the publishers. The book "wasn't really selling. It certainly wasn't doing anything fantastic."

It was a mark of the enduring quality of the first three – Every Light in the House Burnin', Never Far From Nowhere and Fruit of the Lemon – that none had gone out of print. It was perhaps a mark of their limitations that she had not managed to sell a single one abroad. "Middle aged and middle list," she points out. "It's bloody tough out there in that position. They were giving up."

But then came the prizes. First there was the Orange. Even then, she says, Small Island only got a halfway decent bump in Britain, and no one abroad was interested. Then, in fairly quick succession, came the Whitbread, the Commonwealth and the Orange Best of the Best, as well as being shortlisted for the National Book Critics Circle award in the United States, Romantic Novelist of the Year and two National Book awards in this country. The novel – about four Jamaicans who emigrate to Britain during the Second World War – broke through, in a very big way indeed. Translated into 22 languages, from Vietnamese to Macedonian, it became a bestseller both in the UK and Canada and was chosen as the Big Read in Hull, Liverpool, Bristol and Glasgow.

"I'm still reeling from the success of it," she says. "I'm still wondering what it was all about. It got sanctioned as part of the canon. Once I won the Whitbread I could see that it was going beyond what I ever thought was possible. Older white men interested in RAF gunners were buying it and reading it and enjoying it – the kind of people who'd never bought my books before. I wonder whether it was because we'd just gone through this massive period of immigration from eastern Europe and maybe there was safety in looking back at that part of our immigration history with some nostalgia."

Either way the success gave her the space, time and resources to pursue her literary interests more freely. A couple of years ago she joked that she was retiring: she settled into a rhythm of doing the household chores – paying bills, shopping, etc – in the morning and then writing in the afternoon.

"Well, my retirement is from striving," she explains. "Thanks to Small Island, I don't have to pay the mortgage anymore. There's not a day goes by that I'm not grateful I'm in that position. This girl who had 'shop girl' written right the way through her. 'Shop girl,'" she repeats, and acts out writing the words on her forehead. "Now I can explore what I'm passionate about."

Small Island signalled a significant shift in scale and scope from her three earlier works, which were strong, engaging novels drawn from her immediate life experience and with a familiar cast of characters. Each was set, for the most part, in north London, with a working-class, black family whose parents had emigrated from Jamaica. Each family had at least one daughter who aspired to higher education and at least one sibling who did not. The parents, meanwhile, were more interested in keeping their heads above water than in issues of race, racism and class inequality.

Levy calls these books her "baton race". "I'm a writer learning my craft and gaining in confidence or not," she explains. "So that was the person who I was. Then you write the next one. Anyone reading my books could say, 'Well, she got a dictionary there,' and 'She got a thesaurus at this point.'"

She can tell you, almost to the day, when she was injected with the creative adrenaline that produced Small ­Island – it was 1997, and she was judging the Orange prize.

"I suddenly understood what fiction was for," she says. "I had to read books that I wouldn't have necessarily read. I had to read them well and I had to read them in a short space of time. Back to back. Annie Proulx and ­Margaret ­Atwood and Beryl Bainbridge and Anne Michaels – boom, boom, boom. And I started to realise what fiction could be. And I thought, wow! You can be ambitious, you can take on the world – you really can."

Her ambitions took her further and further away in time and place from her own beginnings. Small Island roamed from London to the Midlands to Jamaica and was set during the ­wartime years. Her latest book, The Long Song, is set on a Jamaican slave plantation, Amity, in the early 19th century in a period up to emancipation. It tells the story of a slave girl, July, and the love, envy, intrigue and spirit of playful insubordination, as well as the political resistance and personal rivalries that surround and consume her – an everyday tale of ­ordinary plantation folk a continent and several generations away from where she started out.

While invitations to parties and literary events have been more plentiful in recent years, she has been less likely to accept them. "Something got put to bed with Small Island," she says. "Running to stand still, wanting to be part of that literary thing – all that has left me. I could quite happily not have anything to do with that world now."

Descriptions of her as "angry" (she once said "fuckers" in an interview) or "worthy" are ham-fisted attempts to force racial stereotypes on her that simply do not fit. In person she is both irreverent and somewhat shy. There's an endearing anxiety about her and, because success came fairly late in her career – she was 48 when Small Island appeared – she has remained largely unaffected by her recent renown. When she was close to finishing the novel she woke up one night in a sweat fearing she might lose it. She already kept three copies in her handbag, as well as the one on her computer and the one hidden in her car in case the house burned down. But what, she fretted, if the house caught fire and a spark took the car with it? The next morning she made another copy and sent it to a friend.

"If I go away I send a copy of my work to my agent asking him not to look at it but, should I not return, please to publish it posthumously," she says. "I am forever convinced that I am never going to get to the end of a book, or that I'm going to lose it. I am an extremely cautious person."

When Levy's mother, Amy, was going to marry her father, Winston, in Jamaica, her father's family hired a detective to make sure there was nothing untoward in her family history. Middle-class, light-skinned Jamaicans – Amy was a trained teacher, Winston a book-keeper with Tate & Lyle – they arrived in Britain in the late 40s to discover that none of the privileges they had inherited counted for much in Britain. Her mother's teaching qualifications were not accepted here, so she took in sewing while she retrained. Her father worked for the post office.

Raised on a predominantly white council estate in Highbury, north London, Levy was inculcated with a sense of class rooted more in cultural behaviour than in resources. "I thought we were middle class because we had three meals a day," she says.

Whatever conscious racial identity she had while growing up seems to have been remarkable more in terms of what was to be avoided than what was to be embraced. "I was not at all curious about Jamaica as a child," she says. "We were told, not in so many words, to be ashamed of it." She only discovered that her father came over on the Empire Windrush, when it was shown on television and her dad casually mentioned it while he was ironing.

The London she was raised in was not the multicultural city it is now. "We didn't know that many black people," she says. "There was another black family at my church. But I just used to feel terribly sorry for them because I knew how difficult it was, and we would never have spoken. I'm not proud of who I was then. But I was just dealing with things as they came."

It was only when she went to art college that she encountered the social confidence and material resources of Britain's middle classes. It would be some time before she started to locate herself within the country's racial hierarchies – during the 80s, when London prided itself on equal opportunities, and she was working in the voluntary sector. During a racial awareness workshop her office was asked to divide into black and white, so she went with the whites.

"And everybody said, 'No, no, you should be on the other side,' and it was a bloody shock. I thought black people were doing something somewhere else that I wasn't a part of. I felt embarrassed to go to their side. Not ashamed. I just thought, 'I don't know anything about being black' – I was inauthentic. I was a political person – a left-leaning person; I thought I'd got my politics sussed. And suddenly this thing came along, and I had to learn about it."

When did she work it out? "Any day now," she says, laughing. "I'm still learning."

She points to a boxed set of Who Do You Think You Are?, the BBC TV series in which well-known Britons trace their ancestry, and says, "They'd never have me on because I'm not a big enough celebrity, but I love it. People can go back generations, but they've only done about three black people and they can only take them back so far and then the door shuts, because all that's there are ledgers. Nothing else – just a big mass of nothing. I know my ancestors were slaves, but what did they do? How did they live? How did they manage to survive it? We know so little and very little of what we do know comes from them. The only way you can go any further is through fiction."

This was the curiosity that produced The Long Song, in which July tells her story, urged on by her son. Levy says she was inspired to write the book after a young black woman at a conference on the legacy of slavery rose to ask how she could have pride in her ancestry when all her ancestors had been slaves. "I thought, 'Wow, how could anyone have any shame or ambivalence at having slave ancestry?" She wanted to see if she could change this woman's mind and make her proud of her ancestry.

"When you try to imagine slavery in terms of what happened it's almost unthinkable," she says. "But people got through it. Not every day was: 'Got up, got whipped thoroughly, saw someone hung from a tree'. So I try to give a sense of the daily life – the drinking milk and eating yam of it – as well as the lives of the planter class. I try to give people their humanity."

But she is acutely aware of how the subject matter itself could overpower her literary efforts. When Small Island failed to make the Booker longlist, one of the judges explained that the book was "worthy", but that the acclaim "comes from the topic rather than the treatment . . . People feel guilty about not thinking about our colonial past."

This is not the world that Levy wants to take on The Long Song, and she did not begin with the intention of writing a book set during the time of slavery. She wants her books to be read, she explains, but many people, for different reasons, prefer not to engage with that aspect of their past.

She talks about slavery as though it is a live wire in the public imagination. When people touch it there is a short-circuit; either they think they know all about it, they don't want to know about it or they think that it's not a topic worth knowing about.

"There are a lot of people who are open to talking about it," she says. "But there are many who will say that it was a very long time ago, and a lot who just don't want you to mention it because it will make them feel bad. It's painful, both for black and white people. But it's 300 years. You can't just ignore it. I don't want people to feel guilty. I don't want them to pick it up and feel like they're taking vitamins."

The novel was intended to cover a much longer period of time, she says. "I was intending to get out of there very quick. But you can't avoid slavery. You can't. You have to go to that place. You keep banging into it. I'm not proselytising. It's the book I had to write because of who I am."