It’s not unreasonable to presume that every Beatles story that lives in the memory of their two surviving members has been told. So, when Paul McCartney experiences the Proustian rush of a hitherto forgotten one, you can’t help but feel it too.

Adjourning from the restored windmill that is his Sussex studio, 66-year-old Macca remembers: “There used to be this paper in Liverpool called Mersey Beat. And in it you had a column where you could put personal ads. And so John and George and I used to put them in. Just so we could see our words in print, you know? It’d be like: ‘Barry! Meet me behind the station at this time.’ And then it would come out and we’d be like: ‘Yeah! It got in!’ Just seeing it there was a little kick.”

For once, the word “little” means exactly what it’s supposed to mean. More commonly in Macca-world, the word “little” serves a carefully designed purpose. The Beatles were a good little band; this year’s Anfield show, at which McCartney sang A Day in the Life to 34,000 fellow Liverpudlians, was “a good little show”.

Compacting the details of his world to a manageable size has long been crucial in McCartney’s lifelong attempt to convince himself and others that his days really aren’t too dissimilar to yours and mine. Admittedly, Sunday’s “little” signing event in HMV won’t tilt the world off its axis. But it shows how McCartney can turn the dimmer switch of Beatlemania up or down as whim dictates.

The primary beneficiary of Sunday’s hubbub will be Electric Arguments, the new album that — as the Fireman — he and the famously “cosmic” producer Youth wrote and recorded in just a fortnight. This isn’t the first time the two have collaborated, but, unlike the instrumental electronica of their first two albums, something long believed missing in McCartney has re-emerged. By lurching dramatically from a stoned modern sea-shanty (Travelling Light) to a lysergically progtacular Maori spiritual (Is This Love), it’s closer to the Beatles at their most casually inventive than anyone could expect. How perverse, then, that McCartney should stop short of putting his name to it.

“Actually, I don’t think it is,” he protests. “I’m just doing the same thing I did with Sgt Pepper. It’s just a trick to fool yourself into thinking you’re not you, like a masked ball. There’s something liberating about that.”

After negotiating the legal fallout from his divorce from Heather Mills, the studio must have felt like a place of catharsis for McCartney. Not for Macca and his tiny attention span the claustrophobic soul-searching so necessary to the creative processes of, say, Radiohead. McCartney thrives on speed — more so in times of stress. In 1969, when the Beatles began to implode, it was McCartney who instigated the Get Back project — conceived as a return to the group’s rock’n’roll roots — which eventually became Let It Be. Recording the Run Devil Run covers album in 1999 after his first wife Linda’s death, he laid down two tunes a day. In a week, the record was done.

“You don’t want to take all afternoon just to get a vocal,” he says. I suggest that during his lean 1980s that’s precisely what he would have been expected to do. He remembers being in the studio recording the soundtrack to Give My Regards To Broad Street at the same time as the 1980s pop boffins Scritti Politti. “Were they the band that did Absolute? The guy had apparently taken all week to do his lead vocal. And when it came out, it was like, ‘Well, all right . . . it’s good but . . .’ ” Having recorded his vocals for Eleanor Rigby in one 1966 spring afternoon (with enough time left over to lay down harmonies for I’m Only Sleeping) his air of amused exasperation isn’t hard to fathom.

For all the analysis heaped upon McCartney’s avant-garde tendencies (often at his behest) the experimental bent resurgent on Electric Arguments seems really just a function of that desire to ensure he is having fun. He seems especially tickled by the idea that Girls Aloud record their vocals in tiny chunks, often not finding out what songs their work ends up on until the finished album is played back to them. “I like these tricks, you know. You’ll hear them on a song like Sing the Changes — that Burroughs cut-and-paste way of putting something together.”

Whether we’ll hear those techniques as they were used on the last major piece of unreleased Beatles music is a moot point. Recent reports suggest that McCartney is now keen for people to hear Carnival of Light, the 14-minute “happening” created for the Million Volt Light And Sound Rave at the Roundhouse in 1967. Thirteen years after George Harrison vetoed its inclusion on Anthology II, McCartney intimates that resistance to its release persists. Bad news for the dinner lady at his daughter Beatrice’s school, who read about the existence of the track and excitedly approached him to find out more. “I was like: ‘I don’t think you’d like it.’ People are thinking there’s another Strawberry Fields somewhere [and] you know, this is more plinky-plonky. I mean, I like it, but it’s not to everyone’s taste.”

You get the sense that, at times, McCartney’s thumbs-up, let’s-do-the-show-right-here tendencies must throw up myriad logistical headaches for his band of fixers. His Tel Aviv show in September was a case in point. Talking about doubts cast upon his safety by Islamic activists such as Omar Bakri Muhammed, McCartney says blithely: “I just got a feeling that it wasn’t real. And really, you have to go on feel.” Given the manner of John Lennon’s passing, there’s something remarkable about his almost jocular depiction of the tension between his jittery minders and his desire to roam freely.

McCartney got his wish. “We went through the wall to Ramallah, and we saw Banksy’s graffiti on the Palestine side.” Once there, McCartney and his “team” hastened to one of the pan-Arabic workshops established by the Israeli conductor Daniel Barenboim and the late Palestinian thinker and activist Edward Said. “They get Palestinian kids off the streets and give them violins. It’s the simplest thing, but it’s wonderful.”

Though inspired by what he saw, a return to the 1980s hits such as Ebony & Ivory and Pipes of Peace — syrupy exhortations for a more a harmonious world — seems unlikely. For his next album McCartney says that he wants to to keep “the Fireman spirit”, albeit without scaring the dinner ladies at Beatrice’s school. “That’s definitely the hobby part of what I do. Hearing it back and working out what it means. I’m constantly finding out things about myself.” I point out that the final track on Electric Arguments, Don’t Stop Running, seems a case in point. He sings the phrase of the title so many times that it assumes the mantric air of a cosmic note to self.

“I believe that,” he concurs. “All of it is there for a reason. Even if it’s just to put it out there. Just like we did years ago with those personal ads. After all these years, it’s exactly the same thrill — the thrill of going, ‘I did that’.”

Paul McCartney will be signing copies of Electric Arguments at HMV, 150 Oxford Street, London W1, on Sunday, 10-11am; for admission details visit paulmccartney.co.uk.

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