There’s nothing like making a grand entrance, and that’s precisely what Imogen Heap does as she wafts into the reception of the City apartments she has chosen for our interview. Exuding a combination of bohemian attitude and theatrical style, her outfit features an extravagant necklace of dyed ostrich feathers, printed taffeta skirt, footless patterned tights and pink ballet pumps. Red and black feathers hang from her hair and two sparkling butterflies adorn her left cheek. The concierge raises an eyebrow as he hands the key to this 6ft woman but says nothing.

“I thought seeing as I was going to have my picture taken I’d use the clothes I wore to the Narnia premiere a couple of days ago,” she explains. “They cost an absolute fortune so I want to get some mileage out of them. And it’s my birthday.” Heap’s reputation for eccentric dress sense precedes her. Arthur Boulton, her tutor at the BRIT School For Performing Arts and Technology in Croydon during the mid-1990s, recalls her wearing a different outfit to college every day during her two-year spell there, including harlequin leggings and workman’s overalls. The chichi image is perfect for the quirky but blissful music she makes, yet Heap is also a shrewd operator.

This is the woman who set up her own label, Megaphonic, and released her solo album of sweeping electronic ballads and technopop, Speak for Yourself, using funds raised by remortgaging her flat. Its release in August brought critical acclaim, leading to the invitation to provide the closing song on the big-screen adaptation of C. S. Lewis’s fantasy. The breathless, wide-eyed wonder of the resultant song, Can’t Take It In, suits the movie perfectly, but Heap has one minor reservation about it. “It was wonderful seeing it in context but the credits start to roll as it plays and everyone began clapping so you couldn’t hear it all. I was sitting thinking, ‘Shut up, it’s my bit!’ ”

Expelled from her Essex boarding school at 16 “for pushing the boundaries too far”, she fell in love with electronic music, fuelled by a taste for drum’n’bass raves, and signed her first record deal at 17. She released her debut solo album, the anagramatically titled I, Megaphone in 1998, and then teamed up with Guy Sigsworth as Frou Frou, releasing Details in 2002.

Later Heap decided she would write and record a solo album and then issue it herself. “She’s got this very personalised approach to doing things,” Sigsworth says. “She’s the sort of person who, even if she sold a million records would still send you a home-made Christmas card.”

Now she has a decision to make. The success of Speak for Yourself has inevitably brought the major labels running back. An offer is sitting in her kitchen. “It’s made me really think hard,” she confesses. “I swore I’d never do it again but I’m torn now because, much as I love the control and having everything the way I want it, it takes up an extraordinary amount of my time. I would rather be making music than deciding how many records to press. I don’t want to ruin this album’s chances by being pig-headed.”

Speak For Yourself is out now on Megaphonic