But just a couple of weeks later, the split did indeed happen: Mutya Buena (the perennially scowling half -Filipino one) quit, the reasons proffered gleefully contradicting one another. She wanted to spend more time with her new baby daughter, born six months previously. She wanted to pursue a solo career. She hated her bandmates, and always had done.
"Not true!" laughs Heidi Range (the bottle-blonde one) over orange juice in a west London hotel one Wednesday afternoon. "It wasn't like that at all, honest. OK, yes, in textbook terms, Mutya leaving when she did - well, it was probably the worst timing it could have been, like, but she never hated us. She never actually gave us a reason for quitting. She just went, that's all."
Range, who is perky to a professional standard and has a habit of gazing at you with her cold blue eyes without ever quite pulling focus, smiles blandly: "And then our manager found us Amelle here [Amelle Berrabah, the new sultry one] and it's all really good and brilliant now."
No doubt at this juncture, Keisha Buchanan would have pitched in with her own reading of the situation. Buchanan is, after all, preternaturally ingenue-ish and full of skittish opinion. But she isn't here right now. Why?
"She missed her flight, didn't she!" This from Range. "We were in Italy last night, Turin I think it was, and me and Amelle wanted to come home early today so we could get our hair weaved in time [for the Brit Awards, at which "Push the Button" would miss out on Best Single to Coldplay's "Speed of Sound"]. Keisha was going to come with us, but she never made the flight."
Eventually, I do catch up with the woman by telephone the following day. This is the morning after the night before when, despite losing out on a Brit, Sugababes partied with alcopop-flavoured gusto. As a result, she has all but lost her voice. When she tries to talk, a frog's croak pops out.
"It was a... sh-shame," she says, clearly struggling, "but Mutya wasn't happy, was she? I could see that, but then I've known her half my... half my life." She stops here to ask if I mind whether she whispers instead. Whispering is softer on her voice, and easier too. The words now come out in an excitable rush. "What a lot of people don't know about Mutya, right, is that she has been singing since she was six years old. Before even I met her [at school], I saw her on TV - Michael Barrymore, My Kind of People - singing Whitney Houston's 'The Greatest Love Of All'. Mad, isn't it? I had a pretty normal childhood, right, but I don't believe she had the kind of childhood where she went to school, and that. All she has done is sing, and now that she's 21 and a mother and everything, she probably just wanted a change of scene and I can sort of understand that, can't you?"
Presumably, their decade-long friendship has suffered, though? "Well, we're trying to build on that now. Obviously, when you are in a band with each other it can get a bit, well - you know how things can get. Actually, though, we never really did have arguments, me and her, we just never spoke to one another. We're trying to make up for it now. I think our friendship kind of became broken along the way. But that's the way things go, innit?"
Mutya Buena and Keisha Buchanan met at school in north-west London when they were teenagers, and spent the next couple of years dreaming of pop stardom. With the help of understanding parents, they did everything they could to make it happen, and by 1999 they'd secured themselves a manager, a record deal and a third member, Siobhan Donaghy. Come the following July, when the girls were 15 years old, their debut single, "Overload", reached number six in the charts. But after their first album, One Touch, failed to perform, they were dropped. The band's manager, a shrewd Liverpudlian called Mark Hargreaves, now 42, refused to give up, convinced of their talent. He found them another label, Universal, and put them in the studio with some of the industry's finest pop songwriters and producers. The result? Massive success.
But life as a Sugababe would prove tumultuous. Band tension was forever high, their schedule was ridiculous, and in 2001, during a promotional tour of Japan, Donaghy quit. It was never official; she simply nipped to the toilet one afternoon, and failed to return. Her departure, it was subsequently suggested, was due to the bullying tactics of Buena who, by this stage, had become seen by some as pop's equivalent of Joe Pesci: small and terrifying. Manager Mark Hargreaves barely batted an eyelid. He simply replaced her with fellow Liverpudlian Heidi Range, who had previously been in Atomic Kitten.
He was able to do this so smoothly, he tells me, "because we've always focused on the music with Sugababes rather than them as individuals. We've turned away a lot of endorsement deals and high-profile attachments along the way specifically so we could remain solely about that - the music - because that's where the girls' strength really lies."
Had they done a Spice Girls and lent their names to any old product, he argues, they would have become a far more disposable proposition. Instead, they remained fresh and relevant. "And so to then lose Mutya and be able to replace her as seamlessly as we did, proves that the Sugababes brand, if you like, overrides any single personality."
By extension, then, could he replace every band member for a clone whenever the need arises?
"Well, I don't mean it to sound quite so cold and calculated, and I'm not saying that we'll see Sugababes in 10 years' time in its fourth line-up but, yes, I suppose there is an element of truth to that."
Paul Rees, editor of Q magazine, concurs: "They are almost run like a Broadway musical," he says. "The whole setup is already in place - the songs, the production team - and the management just brings the cast in. Certainly, Sugababes are a step above the norm in terms of quality for British girl acts, but I don't think the members themselves have much to do with that. They are a very efficiently run business, and as long as the personalities within the band are kept to a bare minimum, it doesn't really matter who the members are, does it?"
Whether Sugababes themselves are quite so aware of their expendability isn't entirely clear. It's not that they are stupid - far from it - it's just that they seem either sweetly naïve to the reality of their roles (Heidi Range, for example, insists to me that the band writes its own songs when nothing could be further from the truth), or are perhaps just blissfully uninterested. They became famous after all, that most coveted of teenage dreams, and they get lots of free clothes. Buchanan, for one, adores the position she is in.
"I've always loved the name 'Sugababes'," she gushes, "and I'm so glad to be one of them."
And so what, in all this, of Amelle Berrabah's arrival? A baptism of fire, surely?
"Actually, no," she beams. "So far, it's been wonderful. I did worry initially that maybe - and no offence here, Heidi - that maybe they were going to be bitches to me, but they haven't been - yet, ha ha. They've been completely lovely."
When Buena quit in December, Hargreaves immediately enrolled Berrabah, a 21-year-old from Aldershot via Morocco who had been chasing a solo deal for the previous two years without success. She saw joining the band as a last gasp for recognition.
"I nearly had a heart attack when Mark asked me, but it's a dream come true. Honestly, it is."
Hargreaves decided that for her to feel fully part of the band, she should re-record all of Buena's parts on Taller in More Ways. But, due to their hectic schedule, she had time to complete only four numbers, one of which is the new single, "Red Dress". Play her version and Buena's back-to-back, and it is difficult to hear any discernible difference. It's as if Buena never existed, a fact that probably doesn't augur too well for her imminent solo project.
In July this year, Sugababes will do something no other modern girl pop group has quite managed: reconvene in the studio to record their fifth album. In an industry that treats pop acts as here-today, gone-tomorrow commodities, Sugababes, "the brand", is proving unexpectedly enduring.
"And the atmosphere in this current line-up," says Mark Hargreaves, "is the best it's ever been. It's total harmony."
Good God, I say: how ever will Sugababes cope with harmony?
Hargreaves smiles. "They'll bear up, I'm sure."
Towards the end of my whispering telephone conversation with Keisha Buchanan, I ask whether she ever feels overworked and, just perhaps, under-appreciated. Does she worry that she could find herself, in six months' time, in Mutya Buena's position, replaced, forgotten, discarded? Absolutely not, she responds with typical brio. Everything in life is good, and she mentions the positive things such as stardom and make-up artists and aeroplanes and hotel rooms. And while pop hasn't yet made her properly rich, she is comfortable.
"I bought my own house recently, which is brilliant, isn't it? Of course, I've not bought it outright or anything. I have a mortgage just like everybody else, but that's OK, it keeps me normal." m
Sugababes' new single, 'Red Dress', is released on 6 MarchReuse content