They're the most successful girl group of this century. They've had more original Top Ten singles than any female band since the Supremes. And when you meet the Sugababes - currently made up of Keisha Buchanan, 23, Heidi Range, 24, and Amelle Berrabah, 24, after two line-up changes - it's a shock to realise that, just as the Supremes were, they are still very young. “I didn't even know they carried on after Diana Ross left,” Buchanan admits, observing the Supremes timeline in the new V&A exhibition.

We're looking at frocks in glass cases and pictures of the Motown legends that made up the world of the Supremes. “That's Berry Gordy isn't it?” Buchanan says, pointing to a picture of the founder of Motown Records, then to an adjacent image of Diana Ross. “They had a thing, didn't they, and had a baby.”

The early days of the Supremes and their peers are a revelation to the girls. They express amazement at the stellar line-up on an early gig poster, which features the Supremes alongside James Brown, the Beach Boys and the Rolling Stones. “It's not like those summer festival radio gigs we do, is it?” Range whispers to Berrabah. But they are most taken with the spectacular dresses, pointing and exclaiming at the pale pink numbers that the Supremes wore to meet Queen Elizabeth the Queen Mother, heavy (35lb) with diamante, or a trio with glittering psychedelic swirls and masses of feather trim. “How small the ladies were,” Buchanan remarks.

“They're a lot more glamorous, much more elegant,” Range says, comparing the dresses to the outlandish, almost cartoon-like costumes that the Sugababes have been rocking on their latest tour. Their outfits are all Velcro and zips to allow for a quick change between songs, something the Supremes didn't have to contend with. But one thing the Sugababes do sympathise with is the wear and tear on their “work” clothes - “We've got these ones with Swarovski crystals on them and if you look up close you can see a strip missing,” Range laughs. “You can't tell on stage though.”

The stories of both bands, formed almost 40 years apart, have plenty of parallels. They're not just phenomenally successful female trios. The first incarnation of the Supremes came from the housing projects of Detroit. They were “diamonds in the rough, and Motown had the good sense to polish them,” their stylist, Maxine Powell, is quoted as saying in the book that accompanies the exhibition. Only one of the original Sugababes, Mutya Buena, who departed the band in 2005, actually lived on an estate, but the current line-up retains a certain edge that makes it clear that these are not your average stage-school pop dollies.

Stories in the papers regarding Berrabah's two arrests (the first time she was acquitted of any wrongdoing, and the second time it turned out she wasn't even in the same town at the time), and references to her “Gypsy” boyfriend Freddie Fuller, who was falsely accused of rape by the singer's sister in early 2007 and then fell victim to a near-fatal machete attack at the end of the year, haven't helped. This rough edge seems to add to their appeal, however, and certainly makes them more interesting, just as it helped the Supremes - their girl-next-door brand of fame and fortune seems attainable.

Of course, the most obvious parallel, as Buchanan points out, is the revolving-door line-up changes that now define the public image of both bands. Siobhan Donaghy, one of the first 'Babes, walked out during a Japanese tour in 2001, saying she was going to the toilet. Instead she resigned and got on a plane. She later claimed that she had been frozen out by the other two. Buena followed four years later, saying that she needed to spend time with her daughter, Tahlia-Maya.

Buchanan has gained a reputation akin to that of the young Diana Ross - ambitious, controlling, even scheming. But steely though she can be, she comes across in person as perfectly pleasant. She is reluctant to talk about early strife, but hints that it could be attributed to the girls' youth (they were 13 when they got their first record deal) and manipulation by those around them.

“Unfortunately we probably didn't have that healthy a relationship, and adults at the time... well, you can get the kids to play together, or you can divide them, and unfortunately that's what they did on the previous line-up.”

It was hard for the Supremes in their early years too - they didn't have a hit for four years and were known in the Motown Studios as the No-Hits Supremes. They also found themselves torn apart later in their career, as Diana Ross was groomed for solo stardom at the expense of the other two.

The girls are more comfortable talking about other musicians. Compared with Girls Aloud, Buchanan thinks that the Sugababes are a different proposition. “We haven't sold our records on the basis of what we look like,” she says. “But I think there's a lot of pressure on bands like that because they can't go: ‘OK, I'm going to go without hair and make-up today.'”

Discussing the Supreme Florence Ballard, who suffered from depression and drank heavily, they sympathise with the difficulty that young stars have staying on the straight and narrow - Buchanan has admitted being depressed earlier in her career with the band - but like any good girl band with tweenaged fans, they express shock at the open drug-taking they see in the music industry. They give short shrift, too, to those people who become obsessed with the lifestyle. “There's one girl,” Range says, “I won't say who it is but she asked my boyfriend to hand her a bouquet of flowers, surrounded by paparazzi. He went ‘No', so she got somebody else to do it and then she turned round and went, ‘That worked!' 'cause all the paps took pictures.”

Break-ups, dramas, depression, girl-next-door looks and some seriously catchy songs - if they go on like this, we'll be seeing a Sugababes exhibition in 40 years' time.

The Story of the Supremes from the Mary Wilson Collection, at the V&A (020-7942 2966), until Oct 19

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