Only in basketball would Deng be called a small forward. He is such a good small forward, however, that he has just been signed by the Chicago Bulls for $6.3m over three years. Apparently, the Bulls aren't at their strongest, past the heyday when Michael Jordan ensured that even those who knew nothing about basketball knew the Bulls, but they are still a big deal, and so, suddenly, is Deng. Hence the posse, the 15 minutes of face time I'm told I'll be permitted, and the anxious PR man for PlayStation buzzing around saying, "You will mention PlayStation 2, won't you? Won't you?"

But this is also the gym in which Deng has trained for seven years, ever since coming to Britain in 1994 (and PlayStation 2 sponsors Hosana, an organisation that supports grassroots basketball throughout the UK). This, Deng says, is home, and the observers are two brothers, a couple of guys from Hosana and his childhood coach, Jimmy Rogers, who still teaches the youth of Brixton the joys of bouncing balls. So it is starry and entirely unstarry at the same time, a shambolic collision of NBA control and simple Brixton mess.

In previous interviews, Deng has referred to his family's move from Sudan, via Egypt, as "a tough journey that has helped me mature that much quicker" to seeing "things that a lot of adults have never seen and never will". But when I ask what he means, specifics elude him. "I left Sudan at a very young age, so I don't really remember much." Six years' training in the US has given him a languid American accent. What was life like in Sudan? "To be honest ... " He laughs, rather engagingly at a loss, and I'm reminded that despite the poise, and watchfulness, he is only 19. "I can't ... "

Luol's father, Aldo Deng, later fills in the gaps. The Dengs - Luol is the eighth of nine children, Aldo has two other wives and a total of 16 offspring - were a wealthy landowning family ("We had farms, cars, houses"). Aldo was elected to parliament in 1967, and by 1989 had served as a provincial governor, as deputy speaker (twice), as a minister of culture, of irrigation, of transport, and as deputy prime minister. But they are also Dinka, a southern Sudanese Christian tribe notable for its height, but known mainly in the west for its misfortunes: women and children sold into slavery in Sudan are frequently Dinka.

In 1989, the elected government was overthrown and Sharia law imposed. Aldo Deng was imprisoned for three months, then released on condition that he negotiate peace between the Christian south and the Muslim north. That year, when Luol was four, he took the precaution of sending his family to Alexandria. On December 15, 1993, on the pretext of a holiday, Aldo left Khartoum for London; the following month, he claimed political asylum.

Luol is a bit hazy about Egypt, too. Did they live in a refugee camp? "We were refugees, but I never really went to a refugee camp," then, "not basketball, or any other refugee camp." All the same, in Alexandria they were so poor that the Catholic church had to come to their rescue with food; the Egyptian government provided free education.

What would have become of them if they hadn't left? "The lucky ones would have gone into the army. Others might have died. They would have been mistreated because of my name. So many relatives, so many supporters, have died because of my name."

Another brother shambles in, sits down next to Luol, introduces himself as Ajou, "the tallest one". And how tall is that? "6ft 11in". Four of Luol's siblings play competitive basketball; Ajou, injured a year ago, used to play for the universities of Connecticut and Fairfield, and wants to turn professional; Akuei used to play for Brixton Top Cats; sister Arek, plays for Delaware University; Deng Deng plays for Plymouth.

The family was aided by the appearance one summer of NBA star Manute Bol; a 7ft 7in Dinka who ploughed much of his accrued millions back into charitable causes back home, as well as into the Sudan People's Liberation Army (SPLA). On holiday in Alexandria, Bol saw the brothers knocking a ball about, taught them some rules and became a family friend.

In time the children joined Aldo, and the family has lived ever since in refugee housing in south London on income support, augmented latterly by what the now-grown children earn. "Our family has been supported by British taxation," says Aldo Deng. "All my children have finished university and even I got involved in studying. We are very grateful. We are not like other refugees who don't remember."

They spoke Arabic and Dinka, but initially no English; at home They "mix it up," says Luol with a mischievous grin. "You gotta be one of the family to understand what we're saying, but mostly we speak Dinka."

Basketball in Brixton provided a way of belonging. "You don't need to speak the language," says Ajou. "Basketball got us a long way. It gave us education." By the time he was 13, Luol had been asked to play for England's 15-and-under teams in both football and basketball. Reluctantly, realising he was too tall, "except if I wanted to be a goalie or something", he relinquished football, and later led England to the finals of the European junior tournament in basketball in Poland. Arek has also played for England.

But the only place for an ambitious basketball player to go is America, and both Luol and his sister won scholarships to the Blair Academy in New Jersey, where he was bitterly homesick. By the time he graduated he was ranked second-best high-school player in the country. Recruiters were so keen to sign him up he once even found one lying in wait for him when he came out of the shower.

He lasted only a year at Duke University before entering his name for the NBA draft. This did not make him popular with Duke fans: online message boards are rife with accusations of betrayal and money-grubbing. "Most kids go to school to find a job to eventually support their family, and support themselves," says Luol. "I put myself in that position in one year, so there's really no need to stay the next three years." He does promise that he will get around to graduating at some point.

What, particularly, would have prompted the Bulls to pick him? "If you're just good at one thing you're not really a basketball player," he says. "I can't really tell you one particular thing." "He's very talented," offers Anjou, "but everyone in college basketball is talented. To be better than everybody you have to work hard. That's what he does. He works hard."

They are all proud of him, says Luol, "but in the family you still get treated the same - as soon as you walk in the door you're still the same kid and if you're messing up, your mom is still going to get on you, but when you gotta walk outside the door, and you see your fans and stuff, it's this kind of different world." So he has a lot of fans? "Yeah. So I try to stay indoors with my family."

At the moment, both brothers are jumping through the hoops necessary to get British passports - they would love to play for England in the Commonwealth games in 2006, and in the next Olympics. It also means, says Aldo, that Luol will pay taxes to Britain, and not the States (Luol has apparently refused a green card): "This is the country that rescued us from the most difficult country in Africa," he says; they want to pay something back. The Dengs will at last be able to stop claiming income support, and - though I'm not sure how Luol feels about this - his father hopes he will buy a small shop, to give his other relatives something to do.

And finally, there is Sudan. Ever since he arrived in England, Aldo Deng has, he says, been working to help southern Sudan: he has chaired various charities and reports on human rights for the Sudanese People's Liberation Movement; he has set up the Deng International Foundation to support children, women, schools and healthcare; recently, he has been among those attempting to warn about the severity of what is happening in Darfur. Eastern Africa is a prime training ground for terrorists, he points out, and some are among the Janjaweed. His most famous son also feels a sense of duty: "I'm in a position financially where I could build something or support a kid [in Sudan]. It's not something I would do just because people expect me to. I believe that I can make a difference."

Finally, he is dragged off for a photo shoot with some children at a basketball camp, some of whom, swamped in their strip, barely reach his knees. Far above his head, on the walls of the gym that made him a player, are encouraging slogans. Rough and Ready. Hoop Dreams Reality. Respect Given.