No, you can’t always get what you want. If Mick Jagger had his way, as he generally does, he would have achieved the recognition as a soloist that he has enjoyed for so long as the frontman of the world’s most durable rock’n’roll band. Instead, as he readily admits, he finds himself upstaged by the vastness of the Rolling Stones’ reputation.

This is not entirely fair, even though he is hardly the only lead vocalist to experience a slackening of public interest when striking out as a freelance. There are tracks on his new Best Of album that are just as powerful as his work with the Stones, and all the more fresh for being achieved without his usual collaborators. But it is not the Stones, and therefore not the great global brand that bears his image.

In the flesh, what there is of it, Jagger remains an extraordinary presence, with the tiny-waisted figure of a boy a quarter of his 64 years, a face less lined than the photographs suggest. On the question of how he keeps himself in shape, he insists that he does “a minimum amount of training for the tour, and then a minimum amount of training during it. I am disciplined in what I eat, but I’m not a maniac. My father [Joe, who died last year at the age of 93] was a theoretical teacher of physical education so I was brought up with this attitude that your body has to do a lot of things and you have to look after it. Some of that was bound to stick, but I have to say that it’s a matter of being lucky genetically. Being built this way is an inheritance.”

All this is delivered in the same classless London drawl of his remote youth. And conducted with the brisk, no-nonsense manner of a CEO with a fortune of £200 million and all sorts of projects on the go. Which, in a sense, is precisely what he is. It is he who draws a corporate analogy when describing the near-death period of the Stones two decades ago. “It is like any office, if you like, or like always being on a committee. If you are together for a long time, it is inevitable that you go through ups and downs, and there are many times when you can break up."

This is clearly not one of the dark periods. The Stones have just completed a two-year tour, culminating in a concert at the O2 Stadium in London at the end of August. “Things have gone well,” he says, adding that the eternal question of how long they will keep going is “a function of many things. If you still enjoy what you are doing, and the audiences still enjoy coming, then it’s a two-way street. Beyond that, ‘how long’ is a crystal-ball question.” The band will tour again, he says, even though no dates have yet been arranged.

From a man so aware of the impact of his career, it is strange to hear him speak in rather small and modest terms about his work away from Keith Richards, Charlie Watts and Ronnie Wood. He even underestimates the number of solo albums he has released, putting it at three. There have in fact been four of them, the first being She’s the Bossin 1985, and the most recent Goddess in the Doorway – famously mocked by Richards as Dogs*** in the Doorway – in 2001. He has toured as a solo artist, but just the once, when he played in Australia and Japan. That was in 1987, when the Stones were barely speaking to each other.

“It’s true, it’s true,” he says about the difficulties of establishing an identity away from such a massive band. “But the thing is, you don’t let it influence what you do. It’s not an irony, it’s a fact of life. And it’s really not something you are very interested in when you are making music. It’s of no interest to you whether someone sees you as a singer with a band. You are writing songs and making records because that is what you want to do, and you are not going to be influenced by his or her perception of you.”

If the most famous of his Stones-free recordings on this retrospective album is the 1985 Dancing in the Street with David Bowie – “That was great, it was Live Aid. Spirit of collaboration . . . and fighting over who had best jacket” – then one of the most surprising is the hitherto unreleased Too Many Cooks, which was produced by John Lennon in Los Angeles in 1973 (the masters of which were recently found under the bed of Lennon’s ex-girlfriend May Pang). In the winter of that year the two spent time together on the West Coast, and the owner of a studio called the Record Plant invited them to come and jam on Sunday afternoons. Cream bassist Jack Bruce also showed up, as did Harry Nilsson. It was done in one take, Jagger recalls, “and then we moved on”.

As he still does, despite looking like such a moored figure in British popular culture. Hard to believe it is 40 years since William Rees-Mogg, then the Editor of this newspaper, wrote his famous editorial, “Who Breaks a Butterfly Upon a Wheel?”, criticising as too harsh the penalties handed down to Jagger and Richards (imprisonment with hard labour, overturned on appeal) for possession of drugs.

Today, when this major player in social history reflects on his progress from parent-shocker to Sir Mick, he finds it is “just a very English sort of trajectory, the kind you can see, for example, in probably a lot of politicians in government who started out as rebels”.

The moving-on is expressed not just in the musicians’ nomadic state that he clearly loves, but in his relatively new passion for film production. There was the wartime drama Enigma six years ago, with a script by his friend Tom Stoppard. Now there is the almost complete film of the Stones’ recent world tour, directed by Martin Scorsese. He is also producing a remake of the 1939 proto-feminist classic The Women, originally directed by George Cukor, which follows the lives of a group of Manhattan women.

And there are the women in his own life – the four mothers of his seven children. He still has a flat in Richmond next door to his second ex-wife Jerry Hall, with whom he is said to have a cordial relationship. “I try to,” he says. But it can’t be easy, can it. If band relations are hard, then what price exes? “Not easy for them,” he says with a big, gusty laugh. “No, we’ve got lots to share, so why shouldn’t you get on?”

And there is his present partner, the 6ft 4in fashion designer L’Wren Scott. Present, but also about to become permanent, according to marriage-mongering rumours. “I think we’ll finish on that note,” says the singer, and does so.

The Very Best of Mick Jagger is released on Monday by Atlantic/Rhino

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