The two teenage boys sitting on the sofa opposite are different in almost every way. On the left is James: he’s black, he’s gay, he’s gregarious, and he’s academic. He’s taking three A-levels next summer, and wants to go to university. Daniel, sitting beside him, is white. He’s straight, he’s shy, and he didn’t enjoy school at all. He left after taking GCSEs, and hopes that his next move will be an apprenticeship in engineering.

So, given that they are diametrically opposed, there is one truly surprising thing about James and Daniel. They are twins. They were born on 27 March 1993, the sons of Alyson and Errol Kelly, who live in south-east London. And from the start, it was obvious to everyone that they were the complete flipside of identical. “They were chalk and cheese, right from the word go,” says Alyson. “It was hard to believe they were even brothers, let alone twins.”

The boys’ colour was the most obvious, and extraordinary, difference. “When James was born he was the spitting image of Errol, and I remember seeing his curly hair and thinking – he’s just like his dad. It was another two hours before Daniel was born: and what a surprise he was! He was so white and wrinkly, with this curly blond hair.”

It wasn’t the first time nature had shocked Alyson and Errol. Daniel and James were the family‘s third set of twins: Errol and Alyson each already had a set with a previous partner. Errol’s first set are fraternal boys, Shane and Luke, who are 21; Alyson’s are identical boys, Charles and Jordan, 20. The only singleton in the house is the couple’s youngest child, and only daughter, 14-year-old Katie. “Apart from her, it’s twin city,” says Alyson. “At least life was made a bit easier by the fact that we always had two of everything.”

But it was clear that having one black and one white twin was going to mark the family out, wherever they went. “We’d go on holiday and people would say, ‘Is that one a friend you brought along?'” says Alyson. For Errol the response of strangers was harder to deal with. “People didn’t believe Daniel was mine,” he says. “They didn’t always say anything, but I could tell it was what they were thinking.”

So how does it happen that a white and a black partner – who would usually produce, as Alyson and Errol did in their other children, black-skinned offspring – have a child who is as white as his mum? I spoke to Dr Jim Wilson, population geneticist at Edinburgh University – and his first question was, “What is Errol’s heritage?” Errol is Jamaican – and that, says Jim, is the basic explanation.

“It wouldn’t really be possible for a black African father and a white mother to have a white child, because the African would carry only black skin gene variants in his DNA, so wouldn’t have any European DNA, with white skin variants, to pass on,” he explains.

“But most Caribbean people, though black-skinned, have European DNA because in the days of slavery, many plantation owners raped female slaves, and so introduced European DNA into the black gene pool.

“The thing about skin colour is that even a bit of African DNA tends to make a person’s skin colour black – so to be white, the child must have inherited more of the father’s European DNA with its white skin variants. Added to the mother’s European DNA, this led to a child with white skin – while his brother, who is black-skinned, inherited more of his father’s African DNA.

“The Caribbean father will have less European DNA than African DNA, so it’s more likely he’ll pass on African DNA – but rarely, and I’ve worked it out to be around one in 500 sets of twins where there’s a couple of this genetic mix, the father will pass on a lot of European DNA to one child and mostly African DNA to the other. The result will be one white child and one black.”

Alyson got used to the comments and the stares, the sniggers about their parentage and the “stupid things people said” when her boys were babies; but then, when Daniel and James went to nursery aged three, the twins’ skin colour plunged the family into controversy. “They were at this very politically correct nursery, and the staff told us that when Daniel drew a picture of himself, he had to make himself look black – because he was mixed-race,” says Alyson. “And I said, that’s ridiculous. Why does Daniel have to draw himself as black, when a white face looks back at him in the mirror?”

After a row with the nursery staff, she gave interviews to her local paper and TV. “I kicked up a fuss, because it really bothered me,” she says. “Daniel had one white parent and one black, so why couldn’t he call himself white? Why does a child who is half-white and half-black have to be black? Especially when his skin colour is quite clearly white! In some ways it made me feel irrelevant – as though my colour didn’t matter. There seemed to be no right for him to be like me.”

Daniel and James are listening politely, but with slight resignation, while their mum relays the story – it is clear that, though they are aware that they are unusual, it is Alyson who is keenest on telling their tale. They don’t remember the nursery incident, they say; but nod their heads as Alyson says she took them both out of it in protest.

Primary school passed without colour being an issue: but, says Alyson, everything changed when they went to secondary school. And at this point the boys, too, add their voices: because the racism they encountered there had a huge effect on them, and on what happened to them next.

It all started well, says Alyson. “The school was almost all-white, so James was unusual. But it wasn’t a problem for James – it was a problem for Daniel.

“The boys were in different classes, so for a while no one realised they were related. Then someone found out, and the story went round that this white boy, Daniel, was actually black, and the evidence was that he had a black twin brother, James, who was right here in the school. And then Daniel started being picked on and it got really ugly and racist, and there were lots of physical attacks. Daniel was only a little kid, and he was being called names and being beaten up by much older children – it was really horrible. We even called the police.”

“I was really bullied,” cuts in Daniel, his face hardening at the memory. “People couldn’t believe James and I were brothers, and they didn’t like the fact that I looked white, but was – as they saw it – black.”

It is interesting that it was the white twin, Daniel, and not the black twin who was on the receiving end of racism – but, though it’s counter-intuitive, Alyson agrees that it betrayed very deep-seated prejudices. “Those kids couldn’t stand the fact that, as they saw it, this white kid was actually black. It was as though they wanted to punish him for daring to call himself white,” she says.

While we are chatting, James and Daniel are sitting at opposite ends of the sofa; they give the impression of being polite around one another, but don’t seem particularly close. As Alyson says, everything about them is chalk and cheese: even their body language is at odds – James moves lightly and delicately, while Daniel moves in a more muscular, masculine way. But when Alyson reaches this stage of their story, you see a glimmer of that age-old solidarity where siblings who keep one another at arm’s length, nonetheless pitch in when one of them is threatened.

“I started to notice how angry Daniel was getting at school, how people were provoking him and how he was getting hurt,” says James. “And when he got pulled in fights, I went in too, to help him. I didn’t want to see my brother being treated like that.” James does not look like a kid who would end up in any fight: but, when his brother was up against it, he weighed in – and, says Alyson, the bruises and cuts they both came home with told their own tale.

It is possible Daniel would not have liked school anyway, but being on the receiving end of racist abuse certainly did not help. “I would have left in year 7 if I could,” he says. “But instead, I left in year 11 – and it felt so good to get away.” He moved to a school that was much more racially mixed, and which his older brothers had attended. “People knew I was Charles and Jordan’s brother, but they were fine about it,” he says.

James, meanwhile, stayed on at the old school. “It was fine in the sixth form – things settled down, and I had never been on the receiving end of much racism,” he says.

But at the same time, he was coming to terms with another major difference from his brother – the fact that he is gay. “I knew from about the age of 15, but I kept it to myself for a while,” he explains. “And then a few months ago, it just seemed like the right time to tell my family. I was most worried about my dad, about what he’d say … but in the end he was fine about it.”

Daniel, too, thought it was fine. “It wasn’t as though it was a big surprise. I’d thought it for a while,” he says. “But I said to him, ‘If anyone starts bullying you about it, I’ll be there to support you.’ After all, James did that for me when I was being bullied. If anyone starts any homophobic stuff against him, I’ll be there to fight them off.”

Like all teenage siblings, there is plenty of joshing among the two of them. “I certainly wouldn’t wear James’s clothes!” says Daniel, laughing. “But if it’s the other way round, he’d wear mine!”

“No I wouldn’t,” shoots back James. “My taste in clothes is way better than yours.”

Alyson says that, initially, James’s coming out was a surprise. “We were like, ‘Woa!'” she says. “My big worry was that he’d think he was different, or special, because he was gay – so we said to him: ‘That’s fine, it’s what you are, but it doesn’t make you any more special than the other children in this family.'” Errol says he was proud of his boy for being open and honest about his feelings. “It’s fine; I’m glad he felt he could tell us,” he says.

But Alyson does admit that, just as she once worried about racist abuse being directed at Daniel, she now worries about homophobic abuse being directed at James. “It’s something you think about from time to time, but the main thing I worry about is him staying safe – I want all of my children to be safe, obviously,” she says.

These days the boys frequent very different social scenes. “A lot of my friends are lesbian or gay, and I go to gay clubs, and they aren’t places where Daniel hangs out,” says James. His big out-of-school interest is cheerleading – while Daniel, whose older half-brothers Shane and Luke are both acrobats, loves tumbling. “It’s something I’ve enjoyed for ages – I love the thrill of it, and I love how it makes me feel,” he says. After leaving school he had a spell as an acrobat on a cruise ship, which is where his older brothers also work, but he didn’t stay long. “I thought it sounded brilliant, but I missed my family too much so I came home,” he says. He has now applied for an apprenticeship, and hopes to make engineering his future.

Occasionally, the twins go out together for the evening. “It’s good fun, because we can be drinking in a bar and someone will come along for a chat who doesn’t know we’re twins. And of course they never suspect and then someone else will say, ‘Hey, do you know James and Daniel are brothers?'” says James. “And people never, ever believe it – they always think it’s a wind-up.”

“Sometimes we even get people who say: ‘I don’t believe you! Prove it!'” says Daniel, laughing. “But we don’t care whether they believe it or not anyway – we know it’s true.”

Alyson says all she wants, like any mum, is for her boys to be happy, and to live lives free from prejudice, so that each can flourish in his own way. “Mind you,” she says with a smile, “I do sometimes find myself wondering, now the children are all getting older, what the future holds. There will be another generation eventually – who will that bring along, I wonder?

“Twins are almost a must, I’d say. But the other big thing is: how many white grandchildren will I have? And how many black?” She throws back her head and laughs, and Errol laughs with her. They’re a straightforward, outspoken family, the Kellys: all they’ve ever wanted for their children is a fair chance in life. And if their youngest twins have made anyone think twice about their preconceptions about race and colour, they don’t mind that in the least. “It’s good to challenge people on race and sexuality and other issues where there’s prejudice,” says Alyson. “If knowing my boys encourages anyone to think a bit more deeply about how we label people, then that’s just great as far as I’m concerned.”

The Kellys and their story is told in Twincredibles, part of BBC2’s Mixed Race season in October