'But do you know what no one has ever suggested?" Carly Simon teases. "That it's a girl." It's the great, white, vain (Warren Beatty-shaped, perhaps?) elephant in the room, which happens to be a chilly hotel conservatory in west London. It's like interviewing Colonel Sanders and not enquiring about his "secret formula". It's a subject that can't be avoided. I'll bring it up at the end, I reason. I'll playfully mention that I think "Nobody Does It Better" is the best James Bond song and then in a throwaway fashion, ask "You're So Vain", so it is about Beatty or Jagger, or both? It doesn't quite work out like that, though, and anyway there's a lot more to this prodigious talent than one song, albeit an exquisitely acerbic ("But you gave away the things you loved and one of them was me") and droll ("Well, you're where you should be all the time/And when you're not you're with/Some underworld spy or the wife of a close friend") one.
We meet ostensibly to discuss her new album, Never Been Gone, which reinterprets and pares down 10 of her loveliest songs (plus, two new ones) from a solo career spanning 39 years and is co-produced by Simon's son Ben Taylor (son of James "Fire and Rain" Taylor).
Simon is a formidable presence, her wide smile dominates a striking face and the slim singer looks younger than 64. She's a musician who has been defined – unfairly – by the men she's attracted, a glittering roll-call of 20th-century icons that includes Mick Jagger, James Taylor, Kris Kristofferson, Cat Stevens, and, of course, Warren Beatty. One of her earliest boyfriends, the English satirist and writer William Donaldson, described her as "the answer to any sane man's prayers: funny, quick, erotic, extravagantly talented".
"My mother told me that any man that I kissed I had to be in love with and I kissed quite a few in the Seventies," she laughs. "I was the new kid on the block and they gravitated towards me."
Are most of the men she's encountered philanderers? "All of them," she says. "That's not quite true, but I mean that's what men do. I don't know many men who don't walk down the street and covet at least five women within a 10-block radius, and think about doing something about it."
Simon then launches her vole thesis. "There are two kinds of vole, and the prairie vole I believe is the only monogamous mammal on this planet and who knows why? I would love to study what kind of chemicals a prairie vole has."
However, she is very generous and gracious about all the "philanderers" she's been involved with. She describes Cat Stevens (now Yusuf Islam), which the exquisite "Anticipation" is about, as having "great wisdom" and "his soul is really much more connected to his consciousness than most people I know, but it comes out in a gentle, ethereal, spiritual way. His wisdom goes beyond age".
I tell her a lot of her early songs feel wise like this too and she counters, "That's because I tried to imitate Cat Stevens." She's also very gracious about Kris Kristofferson ("he was absolutely adorable... but we didn't spend a lot time doing domestic duties"), Mick Jagger ("I always think I haven't thanked Mick enough for singing on "You're So Vain"; I don't think it would have been the hit it was without Mick's voice) and Warren Beatty.
"Warren, as everybody knows, is very very attentive, and riveting, charismatic, not any more so than Kris, but in such an obvious way," Simon says. "He was a man who knew he was gorgeous. Kris was a little less sure of himself but Warren is the ultimate man who is sure of himself. There's no one else like him."
When she stopped seeing Beatty after falling in love with James Taylor (her greatest love, first husband and someone she "still loves") he took it on his tanned, chiselled chin and told her to be careful. "Beatty was a man who knew he had 25 women waiting in the wings," she explains.
Simon has noticeably less self-esteem and is notoriously shy of performing live. Thrillingly, three days before we meet I see her perform live to a tiny, intimate audience for the first time for a Radio 2 concert programme at Maida Vale studios, to be broadcast on Easter Monday. However, she admits that "public speaking is her number one fear over death" and that she always has the "feeling I'm not going to be good enough". At one point, to keep her relaxed, rather bizarrely, the house lights are switched off.
The whole time Simon was at school and college she suffered from a debilitating stammer. If called upon to speak she felt like "the light was shining on me and the more self-conscious you are about it, the more you stutter. I had that fear of having the spotlight on me, of being the only one speaking".
Simon, who was brought up in Riverdale, New York, also experienced the death of her father, Richard Simon, at the age of 15. Richard, the wealthy co-founder of the publishing house Simon & Schuster, was "a great pianist" who loved being surrounded by musicians, so the Simon household was always full of fascinating people, including George Gershwin and Rodgers and Hammerstein.
"When I was 10, my father had a heart attack and I knocked on wood 500 times before going to sleep the first time he was in hospital, it was like counting sheep," she says. "But then it dwindled to about 150 times by the time I was 15 and he died and of course I blamed myself for not knocking on wood enough." Simon admits she has "struggled with anxiety and depression" for most of her life and "sometimes it's extremely difficult to leave my bed".
"Considering I have the disease of depression I'd prefer that it was bipolar disorder with the mania element, which I don't get," she claims.
Simon, open and non-evasive on every topic – bar one; the obvious one – defiantly wears her heart on her sleeve; in fact, it's her stock in trade.
"I write about very personal experiences, I don't know of any other way to do it," she says. "I can't not be really neurotic and I can't not write. You feel it's the only thing you can do and it's the thing you're fascinated by."
Did she feel like she had an "old head" when she was young, as demonstrated by singing "These are the good old days" on "Anticipation"?
"It felt funny singing "Anticipation" again, I had such a different perspective when I was in my early twenties," she admits. "How different it was singing 'these were the good old days'. It had an almost pompous air and it turned out I knew nothing back then. I still know very little but at a higher level of not knowing. I was sure of myself then, but now I think these are the good old days and what lies beyond."
The new version of her first hit, "That's the Way I've Always Heard It Should Be", sounds more evocative now, than it did in 1971. A caustic look at marriage, the song has inexplicably been played at weddings in the US.
"This version of the song really tells it like it is," she says. "When I first wrote it I thought it was an unusual thing for people to break up, and now all my friends are divorced."
Simon has been divorced twice, from James Taylor, and from James Hart, who announced he was gay during their marriage. Simon is still in touch with Hart, but not Taylor and this rankles. Simon and Taylor were pop royalty in the Seventies and lived in a gorgeous complex in Martha's Vineyard, which Taylor built. When they divorced in 1983, after 11 years of marriage, which included "wild parties" and producing two children, Ben and Sally, Taylor got the house. However, Simon later bought it back.
"James lived there for a period of time, but he couldn't stand to live there," she says. "His then girlfriend couldn't stand to live there either because the ghosts of me were so powerful. Now the house has different ghosts, namely the ghost of James."
Do you still see Taylor?
"No, unfortunately, and he has two young boys now that I've never met," she says.
It's about now that I decide to pop the question, awkwardly. So, "You're So Vain", I have this theory that it's about three different men?
"Each verse is about a different person. Interesting?" she teases. "But it's not the amalgam of men [David Geffen, Warren Beatty and Mick Jagger] that you think."
Is it just about all men?
"No, it's not just about all men," she smiles. "It's a profile of specific men."
So, it's not about you? It's a foolish question, especially after she's told me it's about specific men.
"I'm not vain enough to think the song is about me."
Before we part Simon imparts her theory on there being two kinds of people.
"I think there are either metallic people or porous people," she claims. "Warren's metallic and Mick's porous. I know more porous people than metallic and I'm attracted to porous people."
She then leans forward and rubs my shoulder – I've been holding on to it for most of the interview – asks me if it's OK, before telling me that she's a porous person and I'm a porous person and implores me "to be kind to her". It makes me feel special and when I leave I take a quick peek in the mirror to see how special I feel. How vain is that?
'Never Been Gone' is out now (Iris Records). The Maida Vale performance will be broadcast on Easter Monday at 6pm on Radio 2