ANGELA McCluskey, once of Glasgow, London, and New York, is in Los Angeles these days. Nichols Canyon to be precise, “where the sixties happened, basically,” the singer says. David Hockney used to live next door.

“Two minutes down the road it’s sex and girls and the Roxy and the Whisky A-Go-Go, but up here it’s heavenly,” McCluskey tells me as she sits in her “tropical treehouse”.

There’s a grand piano in the living room and a poorly husband, the film composer Paul Cantelon, in the bedroom who really should be on a plane to New York to work on music for a film right now.

McCluskey moved in two weeks ago. “I haven’t spoken to anybody for two days, she says. “All I’ve been doing is moving stuff and cleaning. I’m completely in the mood to talk about myself.”

Boy, she can talk. And she has so much to talk about. McCluskey’s story tumbles out in a glorious sugar-rush of namedropping and sarky Glasgow humour. Within five minutes she’s told me about the time she supported Joe Cocker (“All he talked about was his mother’s Shepherd’s Pie recipe.”), her goddaughter Lily Allen and studying at the Glasgow School of Art with former Strawberry Switchblader Jill Bryson.

By the time our conversation ends Michael Stipe, film director Lynne Ramsay, fashion designer Pam Hogg and Marianne Faithfull will all have drifted by in the conversation.

It’s an indication of how plugged in McCluskey is. To put it in mathematical terms imagine her as a woman at the centre of a social Venn Diagram. She is more connected than the internet.

The reason? The way she sings principally. McCluskey has one of those voices that once heard is never forgotten, equal parts gravel and feathers.

Alan McGee, the man behind Creation Records, once described it as “an incredible juxtaposition of the greats: Beth Gibbons, Billie Holiday and Nina Simone,” and for once in his life he possibly wasn’t exaggerating.

This is a woman who was signed to a $1million contract with Geffen for her band The Wild Colonials, earned a Grammy nomination working with French dance outfit Telepopmusik and more recently sang with electronic hip hop jazz duo Big Gigantic. She’s also recorded for Blue Note and even opened Madison Square Gardens for REM.

And yet, it’s possible you haven’t heard it before. McCluskey remains under the radar to many. She is OK with that. Before making it as a musician she worked in public relations for EMI, so she’s seen the fame game. It didn’t appeal. “I don’t mind success, but fame’s horrible. All my friends – Cyndi [Lauper], Winona Ryder – they were all a wee bit miserable. They didn’t really have a life.”

You could never say the same about McCluskey. She grew up in Glasgow singing at family parties but wanting to be a painter (hence Glasgow School of Art). Wanting to be an actress, she fled to London where she worked for the aforementioned EMI and Channel 4 in its early days, did a dance record with Pam Hogg, went to America and never returned.

“My two mates drove me in a 1957 Mercury Wingtip with the roof down along the Pacific Highway and they were playing Nirvana and I was like: ‘F***, I ain’t going back.’”

The Wild Colonials were possibly as close as she came. They were biggish in America. “I did three albums with them toured the world and then I ended up getting another deal with Blue Note and in the middle of that I was with Telepopmusik and that got really big.

“That got too big. We were doing all the festivals with hundreds of thousands of people and I was with 15 French guys on a tour-bus and I was missing my husband and missing my life. I was too old to be on a tourbus, too old to do drugs and get wasted every night.”

And while all this was going on she’s held regular club nights in both New York and Los Angeles. She’s now bringing her big night out format to Glasgow’s Blue Arrow Club. “My band is going to be my husband, a guy called Chris Stills – Stephen Stills’s son – and James Allan from Glasvegas. It’s like a speakeasy. I bring guests up and that’s all I’ve done since day one.”

Indeed. She met her husband Paul in an Indian restaurant. He was playing the piano when she introduced herself. “the first words he ever said to me were: ‘You’ve got the most unique voice I’ve ever heard.’

And I was like: ‘Oh f*** off, that’s the best pick-up line I’ve ever heard.’”

A week later they were performing a show in the restaurant. “I remember sitting on top of the piano and the door opens upstairs and Nina Simone walks in. Nina Simone. And I’m singing God Bless the Child. Paul didn’t even look up, just said: ‘Be professional.’

“And afterwards we met her and she said: ‘You know, you’ve a very good voice. You should sing.”

Angela McCluskey is at the Blue Arrow Club, Glasgow next Thursday.