There are few things in life that make you feel more pathetic than smoking an e-cigarette in front of Keith Richards. I know this because I’m puffing on one when he sways into his suite at the Savoy in central London, looking, I’m delighted to report, like a caricature of Keith Richards come to life. Smouldering Marlboro in one hand, glass in the other, shirt open, tight black jeans encasing legs so skinny you wonder how they support the rest of him, slight though the rest of him is. For all that people go on about the wrinkles on his face, Richards’ physique is a walking advert for the benefits of a diet he claims is largely composed of “meat and potatoes”, vodka and orange, and nicotine: “No, I don’t work out. No, no, no. I mean, I pick up those things” – he mimes lifting a dumbbell – “and go: ‘God, that’s too heavy.’ Then put them down.”

He shakes hands – his fingers are gnarled with arthritis that he insists doesn’t affect his guitar playing and causes him “absolutely no pain at all … I think it came as a result of hitting things, including my guitar.” And then he looks at my vaping device, and his face clouds with bemusement. “Yeah … Ronnie Wood uses one of those,” he says slowly, in a tone of perplexed horror: you would think he was telling me that Wood wipes his bum with his bare hands. “I’ve tried it,” he adds, pulling a face. It didn’t work for him? “Well, I learned that I clearly don’t smoke cigarettes just because of some kind of … oral fixation,” he laughs.

‘God, that year, 1967, we all went off the tracks’ …Richards during the summer of love. Photograph: Michael Ochs/Corbis

A lot of journalists have expended a lot of energy trying to convey the extraordinary sound of Richards’ laugh. The internationally accepted onomatopoeic representation seems to be either “huargh huargh huargh” or “wurgh wurgh wurgh”, but neither really captures its full, wheezing, gurgling splendour: the most lyrical attempt might be Caitlin Moran’s suggestion that, when amused, the septuagenarian Rolling Stones guitarist makes a noise that sounds like “a crow stuck up a chimney”. Whatever it sounds like, you hear it a great deal. Almost everything Richards says seems to come accompanied by laughter, but nothing makes him laugh harder than the subject of his announcement that he was going to retire. This apparently happened four years ago: it’s mentioned, almost in passing, by Steve Jordan, the producer of his new solo album, Crosseyed Heart, during Under the Influence, a Netflix documentary made to accompany the album’s release. “Well, I don’t know, I did feel at a bit of a loose end at the end of the whole thing of writing and PRing Life [his autobiography], which was probably 2011,” he says. “I thought, ‘Oh, write a book,’ you know, tell a few stories. I didn’t realise that by the time you come out the other end you feel like you’ve lived your whole life twice. And for my life, that’s pretty tiring and a bit confusing. And also, there was no sign of the Stones coming out of hibernation. So I threw out that statement, it was only once that I said it, just to see the reaction it got, really just to punch the Stones in the back of the head. Oh, I’ll use every ploy in the …” he starts to say, but the rest of the phrase is consumed by laughter.

The first person to take the bait was Jordan, the drummer on both Richards’ previous solo albums, 1988’s Talk is Cheap and 1992’s Main Offender. He suggested the pair go into the studio together to “kick some stuff around” in the way Richards and Charlie Watts used to in the 60s and early 70s, a style of working that produced Jumping Jack Flash, Street Fighting Man and Happy. Crosseyed Heart was the unexpected result. “And then, funnily enough, within a few months, the Stones want to get back on the road again! Yeah, disguised as a 50-year anniversary! So it did its kick. I mean, I really hate to tell lies, but that was one of them.”

Galvanised by Richards’ threat to pension himself off, the Rolling Stones are apparently due to go back into the studio soon to make another album, their first in a decade: “They need to, it’s been too long.” In the interim, he seems to be having a high old time promoting Crosseyed Heart: throughout the summer, he has kept news pages busy giving interviews in which he expressed some fairly robust opinions about Mick Jagger (“such a snob”), Bill Wyman (“a funny old fucker”), hip-hop (“so many words, so little said”), heavy metal (“a great joke”) and the Beatles’ Sgt Pepper (“a load of shit”). Meeting him in person, you do find yourself wondering how many of these pronouncements arrived accompanied by a gale of wheezy laughter that suggested Richards might not be talking in deadly earnest; either way, he is clearly in more conciliatory mood today. He starts telling me about a magazine award he picked up earlier in the week – “for being a legend or an icon or an iPad or something” – opining that such things are “all pointless and redundant”, before correcting himself: “Genuinely, I was very touched.” He is still adamant that most rock bands can’t play properly – “they’ve got that sort of European way of looking at rhythm and usually it’s Prussian, it’s like a march” – and he isn’t terribly enamoured of “damn synthesisers and people playing a drumbeat with their fingers”, but nor is he quite as dismissive of modern music as he sometimes appears: “I’m interested in what people think is progress.”

He says making solo albums gives him a greater understanding of “the perils and difficulties of being a frontman” and how good Jagger is at it, “although it’s sometimes hard to pay Mick a compliment. I don’t know if it’s reticence or whatever, but if you say: ‘Mick, that was fantastic’, it’s: [he adopts a diffident voice] ‘Oh, thanks mate.’” And he is keen to underline that the point he was trying to make about Sgt Pepper was that the Stones’ response, 1967’s Their Satanic Majesties Request, was “far worse”, the era of love and peace not really suiting the Rolling Stones. “God, that year, 1967, the effect of LSD on people’s music and lives. People dropping out and going to India! And the Maharishi …” – his voice trails off and his face forms itself into an expression that suggests Richards ranks the founder of Transcendental Meditation right up there with the inventor of e-cigarettes. “I just saw people losing their thread. That year, we all went off the tracks. It was a kind of mad vacation. When we made Beggars Banquet the next year, I felt like: ‘OK, hols are over, old boy, let’s get back to business.’”

‘I’m flattered that old Keef’s become that sort of cartoon figure’ … playing Glastonbury, 2013. Photograph: Alicia Canter for the Guardian

He seems touchingly proud of Crosseyed Heart, despite his continued insistence that he has no interest in being a solo artist: “My whole thing has always been a band, that I’ve got this incredible band that have obviously proved through the years they can hop generations, and, you know, I kind of think that’s enough for one man to ask for and I only do solo stuff when there’s nothing on the horizon, basically, to keep my hand in.”

Nevertheless, Crosseyed Heart is warm and relaxed and possessed of a ramshackle charm noticeably absent from the last Stones album, 2005’s A Bigger Bang: it offers covers of Leadbelly and Gregory Isaacs, and his own Nothing On Me, on which Richards defiantly ruminates about the 1977 Toronto drug bust, for which he narrowly escaped a prison sentence. “It took me a while to realise how much the cops cropped up on this record, on Nothing On Me and Robbed Blind. Then I put it down to the fact that they’d played quite a large part in my life. And, you know,” – he lowers his voice to a mock-conspiratorial murmur – “they did give me quite a bother. They were trying to do me in the early 60s, before there was anything to do me for. I don’t know if I shone out on the street, or trying to creep around the corner. And then later, the Chelsea police force … I’m only happy to say that the guys that did all of that ended up in jail. But it does sort of give you another way of looking at life, when the first thing you do in the morning is look out of the window and go: ‘Yeah, the unmarked car’s there.’ For Christ’s sake, you know what I mean.” Another laugh. “Now, of course, they work for me. I’ve got detectives in New York who take care of me. I suppose it’s the amount of time that’s gone by, and also I think probably because all of their attempts to put me away always ended up in disaster for them. I mean, how many lessons do you need?”

Of course, having “quite a bother” with the police is part of the romantic and enduring myth of Richards as a kind of permanently dissipated musical outlaw and bete noire of polite society, the knife-carrying “living embodiment of rock’n’roll” as one profile breathlessly put it. It is an image that has served him well over the years, inspiring countless guitar-slinging imitators and Johnny Depp’s portrayal of Captain Jack Sparrow alike. But at 71, and not so much a bete noire of polite society as a beloved national treasure (“Am I? I think that’s just a matter of hanging around long enough, you know”), he claims to be tiring of it a little. In Under the Influence, he claims his public image is “a ball and chain”, which feels a bit ironic given that the documentary’s very title plays on it. “What? ‘Keef’? With the bottle of bourbon in one hand and a joint in the other? You do drag it around with you. In a way, I’m flattered that old Keef’s become that sort of cartoon figure. I guess what I mean is that when I meet people in an art gallery and I’m talking about Caravaggio with them, they go: ‘Oh, we thought you’d be different.’ Then it feels like a ball and chain.”

‘I’d like to live another 25 years’ … with Ronnie Wood in New York, 1980. Photograph: Gary Gershoff

Was it an image he deliberately cultivated? “I didn’t mean to. I suppose unwittingly.”

Oh, come off it. In his autobiography, he said he once cleared a hotel room of unwanted guests by getting a gun out and firing it through the floor.

“Well, yeah.” Another laugh, this time a bit sheepish. “In that respect, I see what you mean. Let’s say I didn’t do anything to prevent it. And I suppose it does come in handy every now and again when, whatever the situation is, Keef’s here and there’s already a sense of intimidation or something. But the hotel room … it was one of those days.” He shrugs. “I mean, what do you do when people won’t listen to you? I also knew that the room below was empty,” he adds, lest anyone think that by shooting a gun in a hotel room full of people he was behaving recklessly.

Indeed, so pervasive is Richards’ image that it’s still hard to imagine him doing anything vaguely normal. So what does he do at home, when he’s not being Keef? “I watch the wife garden. She loves to prune things sometimes, and I sort of sit there and go: ‘Oh, you missed a bit.’ I might get the hose out, do a bit of watering. God, I just do what any other old bloke does. I make sure the dogs are fed, I try to live as normally as possible. Actually, I love my old lady, and she can make me do anything. And, hopefully, I’m a pretty good grandad, because they also seem to like me. Fascinating to watch the grandkids, because there’s five of them and they’re all various ages: the oldest is 19, the youngest is two. And so far, they like me. I don’t bribe them. I mean, every grandad has to be indulgent, right, up to a point. But it’s not like ‘Grandad’s arriving’, like I’m Father Christmas or something. I feel privileged, really. I mean, a lot of people say I shouldn’t be here, but I am, and I’m trying to be as good a grandad as mine was to me.”

Yes, he says, he still has ambitions: he would like to make at least one more Stones album, for one thing. “And apart from that, I’d like to live another 25 years or something. I could handle that. I mean, I’m blessed with being sort of physically robust. And what you realise when you get older is, you never stop growing up. You can let other people think you’re grown up, with all this wisdom – ‘Yes, that’s right, my son’ – but, you know, that’s only because they’re younger than you, so you can lay that on them.” Yet another laugh. “Obviously, I have got a bit wiser, I’ve learned a bit more about … pacing myself. But other than that, I don’t think you stop growing until they start shovelling the dirt in.”

Crosseyed Heart is released on Virgin/EMI.