In a backstreet in the west end of Glasgow, rain is bouncing off cracked paving slabs. Black puddles are forming in front of an anonymous building with a steel door. It’s hard to imagine a scene further removed from sun-caressed Los Angeles. Yet behind that door, sitting at his piano, is one of the most sought-after men in Hollywood.

Step into the building and you leave sodden Glasgow for California. The reception is hung with international music awards — a Golden Globe, an Ivor Novello, a Bafta. Beyond is a bright and airy recording studio with pale cream walls. It contains a baby grand piano, a scattering of expensive guitars and maybe 10 different kinds of synthesizer. Along one wall is a 48-track mixing desk and a huge wide-screen television.

In the centre of the room, one hand idly running over the keys of an electric piano, is Craig Armstrong, a 46-year-old Glaswegian in a black leather jacket and jeans.

He starts to chat about a recent job he did in Paris with his friends Nicole Kidman, the actress, and Baz Luhrmann, the director. The three found success together in 2001 with the Oscar-winning musical Moulin Rouge!, for which Armstrong won his Golden Globe as composer and arranger. The team had reunited to make an epic cinema advert for Chanel No 5, set to an Armstrong variation on a Debussy melody.

“We all ended up in the designer Karl Lagerfeld’s house in Paris. It was all very chichi,” says Armstrong with a smile. “My wife was very happy when I got home, getting the free gifts from Chanel. Not a bad thing at all . . .” Armstrong grins the shy grin of a man who is living the good life and knows it. Album sales of the Moulin Rouge! soundtrack topped 15m worldwide, so he is not short of cash.

His burgeoning wealth was apparent recently when he was drawn into a bidding war for the most expensive home in Glasgow, a £1.9m town house not far from his west end studio. He lost out to Robert Carlyle, the actor.

Nicole, Baz and Karl are not the only stellar friends he has made in 15 years of composing scores for some of the biggest names in cinema, with credits including Love Actually, Romeo + Juliet, The Bone Collector and The Quiet American.

Recently he helped out Yoko Ono on a couple of songs she recorded for Amnesty International. David Bowie, Madonna, Bjork and Bono are musical collaborators. George Martin is a pal.

Then there are the friends he made in the pop world as a member of Scottish bands such as Hipsway, the Big Dish and Texas — he co-wrote the latter’s breakthrough hit, I Don’t Need A Lover.

There is also his work as co-writer and arranger with Massive Attack, the most influential British dance act of the 1990s.

With such achievements to his name it seems strange to talk about Armstrong as someone who has failed to get the recognition he deserves. But in the film world there are those who regard it as scandalous he was denied an Oscar for the score of Moulin Rouge! — his lush settings of classic hits were the backbone of the film.

Nor has he truly had his due at home. While Britain’s writers, actors and film directors are held in public regard, mention his name and you will get the response: Craig who? Largely, he says, this is down to a peculiarly British attitude towards his trade.

“In the US and France they have a different approach to film music than in Britain,” he says, without apparent rancour.

Times Recommends

• An officer and a gentle woman
• Dame Helen Mirren is worthy of the Epidaurus
• Foods that can help to prevent swine flu