The 27-year-old songwriter cuts an imposing figure, not least because of her 6ft frame. The Brit-school graduate and ex-Frou Frou singer is the epitome of elegant bohemia and everything about her is stamped with a delightful girly eccentricity. From her butterfly-clad hair and her flouncy gold skirt to the furry red sash that cuts across her body, Heap wears her stylish flamboyance with the confidence of a matador.
She is certainly hard to ignore. Which has also been the case for her startling new single, "Hide and Seek". The hair-raising electro a cappella, taken from Heap's excellent second solo album Speak for Yourself, is an underground sensation threatening to flood into the mainstream. The stark, haunting song was used to soundtrack the emotionally charged series-end of the hit American TV show The OC.
Anticipating a surge of interest, Heap made the track available for download through her website and Apple's iTunes store as the episode aired in the States. Sure enough, the song topped iTunes' electro download chart within hours and has been causing a stir ever since. Radio 1's notoriously enthusiastic Zane Lowe was moved to call it "the hottest track in the world today", while its debut on Jo Whiley's Radio 1 show preceded a leap into the British iTunes Top 10.
"I have to admit, I was rather obsessively refreshing iTunes' chart," recalls Heap, sipping cranberry juice at the National Film Theatre's South Bank café, one of her favourite London spots. "I was watching it, thinking, it's still at No 8, it's still at No - it's at No 7!"
The singer deserves to savour her achievement. In a move that in effect raises two fingers to today's overbearing record companies, Heap has written, recorded, produced and bankrolled her album, under the auspices of her self-funded Megaphonic label. Why? "Because I wanted to find out for myself what I was capable of," she says.
Frou Frou, Heap's icy electro-pop collaboration with the Madonna producer Guy Sigsworth, left her with a burning desire to prove herself. "I loved working with Guy," she says, "and I learnt shedloads from it, but I was sick of people assuming the man did all the music. To the outside world I just looked like the singing girl. I'd do interviews and people would only ask me questions about my fitness regime." She giggles at the memory. "That really annoyed me - Guy and I made all the music together."
This time there is no question about who has done what. As the title, Speak for Yourself, suggests, Heap is responsible for every note on her album. Utilising the knob-twiddling skills she has been nurturing since adolescence, the classically trained pianist recorded all the live instruments, string samples and random noises (trains, crashing kitchen pans) on her Mac. The same goes for her morphing, multi-octave voice, which she uses as though it were just another instrument from her box of musical toys, layering breaths, sighs and whispers to striking effect. It is a hard task, but Heap has succeeded in giving her electro album a human heart.
When it came to dealing with record labels, it was a case of twice bitten, thrice shy. Heap signed to Almo for her 1998 debut, I Megaphone, and then with Universal to release Frou Frou's 2002 debut Details. But both experiences left a bad taste when the companies failed to live up to Heap's expectations. "I was sick of having my hopes fall apart because attentions were diverted to bigger acts. I couldn't bear to have that happen again," she sighs. "Now at least I'm in control."
From hiring the album's artwork photographer (an amateur who calls himself Lomokev, whom she found through the online photo sharing site Flickr) to overseeing the record's distribution, Heap has her finger in every pie - even personally wangling that priceless exposure on The OC. During our interview, a courier delivers a parcel of "Hide and Seek" promotional DVDs which, after our chat, Heap will hand-deliver to Radio 1.
"I suppose I am a bit of a control freak," she admits shyly. "But why should I get anyone else to do something if I can do it myself? I get to have everything done just like I want it."
Such freedom has come at a price. Heap was forced to remortgage her Waterloo flat to pay for her recording equipment and the rental of her Bermondsey studio - a rough and ready, bare-brick room decorated in Heap's image with sorbet-coloured chiffon, cuddly animal prints and dainty fairy-lights. The nagging debt wasn't always conducive to creativity, however.
"There were times when I really couldn't finish a song, when all I could think about was that I'd wasted £2,000 in studio rent," says Heap. "Without anyone to help, I just couldn't imagine how I was going to get out of that fix."
But Heap's determination not to allow anyone else into the studio actually worked well for her - particularly where her songwriting is concerned. Beneath Heap's in-control, determined shell lies an emotional - and, she admits, at times irrational - core. "I have a tendency to get carried away," she says. "I might think fleetingly that someone I know might die, then the next moment I'm crying like it's just happened. And that's exactly how a song might start."
With no one around, Heap felt able to open up. Consequently, from cheeky romantic daydreams ("Goodnight and Go") to intentionally non-specific heart-stoppers ("Hide And Seek" and the album closer, "The Moment I Said It"), her songs make for intriguing and refreshingly human, personal vignettes.
Making Speak for Yourself has been a voyage of self-discovery. Heap has had to learn to rely on herself - both artistically and financially - and to trust her own judgement. Setting out to make a record completely on her own was a risk, but as the album proves, it was worth taking.
Response has exceeded expectation: the first pressing of 4,000 copies sold out in under three weeks; a major label is so impressed that it is offering Heap a deal to sign others to Megaphonic; and requests for her to produce other artists are already trickling in. But most significantly, Heap has proved that you don't need a multimillion-pound recording or marketing budget to make an impact.
"I really didn't expect to get as far as I did," she says. "My credit cards are maxed out and I owe all this money to my mortgage, but I'm really glad I put everything on the line for this. I did this to show people what I could do, but I also needed to show myself. I'm really proud that I followed this through, that I didn't give up and that it's come good. I wanted to do something, passionately, and I did it."
They are heartfelt words, weighted with palpable relief. But she need not have said anything. Her glowing smile speaks for its self.
'Speak for Yourself' is out now. The single 'Hide and Seek' is out on 26 SeptemberReuse content