Soul survivor: Marianne Faithfull gets by with a little help from her friends on her latest album

Marianne Faithfull is standing on my doorstep, and she isn't wearing any make-up, not a tiny scrap. She looks fabulous, but in a downbeat, quiet way. The 62-year-old singer-songwriter is trying out a new technique on me, because she's been wondering if maybe it doesn't help to paint on a brave front when she's being interviewed.

"Oh, you know what?" she explains. "I get all dressed up with that Marianne Faithfull face, and the next thing I know I'm blurting out things that I shouldn't, trying to get attention when, really, I've got everybody's attention already." She laughs, briefly, then retreats back into her pensive mood. "This way, I end up talking about the music instead of about all the other stuff. Anyway, you're my friend. You know all that stuff, and you know what it's OK for me to say and what would get me into trouble."

And because I've known her for years, I know also that she's not – perhaps surprisingly, as she's been feted as a great beauty for all of her adult life – particularly vain about her looks. Once, not long after she'd moved to Paris, she came back to London to have some work done on her wisdom teeth, and stayed at my place to convalesce. The operation made her look as though she'd been punched in the mouth, and I was amazed when she got up and went out after a day in bed, looking like she'd just done five nights in Vegas – and not as a singer.

Faithfull's still wearing the rest of her grande dame uniform, though – thick gold hair (styled by her friends and hairdressers since the Sixties, Keith and Leslie at Smile), and tailored black and white clothing, often from Chanel (she has a comprehensive collection of little black jackets hung neatly in her rented flat behind the Crillon Hotel). Today, she's got a black coat on. "You like it?' she asks. Then she blurts, with unseemly triumph, even after all her good intentions on blurting: "It's Louis Vuitton! He gave it to me!"

Faithfull quite often gets given things. Mick Jagger, Keith Richards and their manager Andrew Loog Oldman famously gave her her first song, "As Tears Go By", when she was 17. Francis Bacon – and others – gave her square meals in fancy restaurants when she was living on her Soho wall, doing heroin, not so many years later. Some other benefactor gave her the cottage in Ireland that she lived in in the aftermath of all that, as she tried to work out what a normal life, for her, might look like.

Inspiration on that one never really struck, and when the Parisian impresario François Ravard turned up one day – himself formerly a teenage runaway from provincial France, and a young protégé of Serge Gainsbourg – he found that Marianne was stony broke but still persuading the not-so-local mini-cab company regularly to bring her fags. He's been her manager, friend and confidant ever since, and she relies on him hugely. Ravard helps her to do what she realised had to come first – work. "I've got a lot of little compulsive problems, and I've thought about it a lot," says Faithfull. "And one of the things I ask myself is, 'What are the things I can do that won't hurt me and will help me?' The first answer is work."

Marianne, despite her reputation as a diva with a Lazarus-like gift for survival, has her vulnerabilities and the business acumen of an odd sock. Despite her steely dedication to protecting the posh and affluent Faithfull brand, she's never had any capital, and has had to graft for a living anyway, even if she didn't want to. Luckily, she also has built-in orphan power, and people often want to look after her. It doesn't take much to make her happy. Ensconcing herself in my living room, she's delighted beyond all sense that I've remembered she prefers lemon and ginger tea.

On her 2002 album of original songs, Kissin Time, Marianne sings a song written for her by Jarvis Cocker, called "Sliding Through Life on Charm". That one line came from her, the rest came from him, and that's very Marianne. Most songwriters, frustrated by a refrain they wanted to use and couldn't get to work, would just shelve it. But when you really are used to sliding through life on charm, you sit down, have a think about who might be able to crack it, call him on the phone, and in no time at all he gives you a song.

Faithfull's prowess with the telephone receiver is legend in itself. She can stay on the line for extraordinary lengths of time, like a teenager. When she tells me that she and Hal Willner, the producer of her new album, Easy Come Easy Go, spent six months on the phone prior to making the studio recording, I have visions of the poor guy sitting there in New York wondering if he would ever have the use of both hands again. "It's Hal's favourite, too," she says in her defence, "just sitting around talking, especially about music."

But they did the right thing, the two of them, because Easy Come Easy Go, her 22nd album, is quite different to any record Faithfull has ever made before, even her previous interpretative studio album with Willner, Strange Weather. All the talking, all the thinking things through in advance, has paid off. But as is often the case with Faithfull, it was the logic of the situation she found herself in, as much as any clear creative game-plan, that honed her focus.

Marianne's life, no matter how much her friends support her, tends to go in cycles. In the 1990s, she'd enjoyed a long period of personal and professional good fortune, in which she published an acclaimed autobiography and released several very fine albums, including Before the Poison, widely regarded as her finest since 1979's Broken English. She also, among other things, toured the world singing Kurt Weill interpretations, recorded her own version of the opera The Seven Deadly Sins, starred on stage in Bob Wilson's production of The Black Rider, and appeared in several movies. But, since Before the Poison came out in 2005, things have been harder in all sorts of ways, some little, some large, but all conspiring to get her down, and mess with her head.

Consequently, her last world tour was beset with disruptions. First, there were cancellations because of a panic attack – reported unhelpfully in the world press as a heart attack and spawning a flurry of worried calls from other venues booked for later in the tour, demanding to know whether they were going to be cancelled.

Then, after the show had been back on the road for a short time, Faithfull found a lump in her breast, and the tour faltered again. The lump itself was benign. But Faithfull did still have breast cancer, unrelated to the lump, and deep in the tissue. It was found incredibly early, and the treatment was much less draining than it could have been. So, as tours cost a lot more to cancel than they cost to postpone, Faithfull, after she had the all-clear, went on the road again. It was too much for her, really.

"I had a lot going on in the last few years, and I think maybe I was beginning to get a bit depressed," she admits. "That's not a good place to write from. Yes, I can write tragic songs, I always love that. But actually I prefer to be feeling rather good and quite perky inside and then I write better, and it doesn't go overboard.

"So with all that, maybe my V C breast thing, maybe all that just caught up with me, and Hal Willner and I had been talking for a long time about wanting to make another recording of other people's songs. I didn't want to do it for a long time, first of all because I had so many ideas for songs and secondly I wanted a long time to elapse between Strange Weather and this next project. It's 20 years now, and I reckon that's a long time, so we both said, 'Let's do it.'

"I started collecting songs myself, and Hal said he was collecting them too. Hal came over from New York to Paris with a lot of material, and I already had quite a lot of material, and we sat around for about 10 days shooting the breeze, listening to music, making our minds up.

"We talked about what we were going to do, and how we were going to do it. One of the ideas was... [For] Strange Weather, we sort of threw it together, really. We picked the songs very carefully but then there was only one song on the whole record that was arranged – 'Boulevard of Broken Dreams'. The rest we worked out more or less in the studio, and that is a very valid way to record.

"This time, Hal said we're going to get really good arrangers and we're going to know what the arrangements are before we go into the studio, which is already a big change, and I kind of wish I'd done this a long time ago. It's the first time I've ever worked like that and I like it very much. This whole experience has been quite extraordinary, and I'm enjoying it a lot."

One of the lovely things about the album is that quite a few of the songs are half-forgotten, and have been revived for the release. This is particularly true of the title track. "Well, I'm not George Melly, who's the greatest, but I love George Melly," says Faithfull, only a bit mystifyingly. You get used to her discursive way of talking, and tend to roll with her as she gets to her point.

"George knew so much about Bessie Smith, and I would bump into him, all my life really, until he died, and we would always talk about Bessie Smith. She was known as the Empress of the Blues and therefore she wore ostrich feathers. And such. You know, I love Bessie Smith, I love Ma Rainey and I love Memphis Minnie, but, of course, most of all I love Billie Holiday.

"But I used Bessie's style – not directly – in my more difficult years when I was touring little places in Ireland where people were having fights and knifing each other, and no one was listening to me. I would cheer myself up by playing certain Bessie Smith tracks. There were literally glasses breaking, people fighting, the most horrific things going on in the background, and she simply didn't turn a hair – and that was my lesson. If Bessie Smith can do it, so can I. And I was looking for a Bessie Smith and I – well, I can't say I was particularly busy, but I was recovering from various things and I asked Poppy Lloyd to help me and she found 'Easy Come, Easy Go' and it's perfect."

I've no idea who this Poppy Lloyd might be. Clearly, in this context, she's just one of those people who don't in the least mind hanging out with Marianne and helping her out when she needs it. On Easy Come Easy Go, Keith Richards, Rufus Wainwright and Nick Cave are among the others who oblige.

Richards, of course, is a very old friend, from the earliest and most highly documented period of Marianne's fame. She got him on board for Easy Come Easy Go so that she could recapture a memory of him, the one that she says is among her most precious.

"The first time I heard 'Sing Me Back Home' was in the Sixties, when I was hanging out with Keith and Gram Parsons. They were going through a big country thing and they were only playing country, lots of Merle Haggard, and one of the Merle Haggard songs they were playing was 'Sing Me Back Home', both playing guitars and Parsons doing the high harmony and it was just so good that it stuck in my mind.

"Also then, while he was going through the aftermath of a drug bust in Toronto, Keith did a bootleg. He went into the studio on a piano and just sang all his favourite songs. He sang The Everly Brothers, George Jones, Merle Haggard, all sorts of people. It was absolutely wonderful and I've got it on CD. It's called Unknown Dreams and it's just as if he's alone, and one of the songs he does is 'Sing Me Back Home'. It's sort of how I see him, Keith, my guitar-playing friend. So it was great to record it with him, for this album."

Other songs, she admits, she would never have thought of recording if it hadn't been for Willner. "He asked what was the first musical I ever went to see, and I've hardly seen any musicals. But actually, when I was eight, Grannie Faithfull took me to see West Side Story. Then he said, 'What were the songs you really liked?' At first I said, "America"! But I remembered that my favourite had been 'Somewhere', and we did it.

"I'm not always the one to know – although I did pick 'Lucy Jordan' and 'Working Class Hero' myself, so I'm not such a fool. And I think one of the best picks I ever made was to pick 'Tower of Song', with that wonderful verse – 'I was born like this, I had no choice. I was born with the gift of the golden voice.'"

Leonard Cohen's lyric is usually interpreted as slightly sarcastic, since his own voice is so famously gravelly. And that's what appeals to Marianne, too. She credits "DJ Bob" for her rendition of "Black Coffee" on Easy Come Easy Go. "I was listening to 'Coffee' on Bob Dylan's Theme-Time Radio Hour and he played the Bobby Darin version of 'Black Coffee', and that was such a great thing for me because I'm intimidated... I love Ella Fitzgerald, but I'm intimidated by her. She's such a virtuoso, and I know I've got an OK, interesting voice, but it's not like that. I know that."

And there we have Marianne Faithfull – not hung up on her looks, and not too carried away with the idea of her "golden voice", either. Essentially, she's a woman who works very hard at making the very best of what she's got, and is always slightly surprised when things start turning out well again. That's what makes people feel so tender towards her. She's eternally surprised and perplexed when she finds out yet again just how special she is.

'Easy Come Easy Go' is out now on Dramatico. Marianne Faithfull plays the Royal Festival Hall, London SE1, on 20 July