"It's very difficult to remember those days because it was all a bit crazy and everyone was getting out of it," the 50 year-old songwriter said. "But yes, John was doing some recordings in Los Angeles and I showed up."
Sir Paul has been irked by received pop wisdom that the songwriting pair were two sides of the Beatles coin who had little in common. Release of the three-part out-takes Anthologies over the last two years had helped redress the balance, he said.
"The Anthology, particularly 3, tends to knock that rumour on the head. You can hear me and John having a good time. You can hear that we are enjoying each other."
He still grieves for Lennon, shot dead by a deranged gunman in 1980, he said.
"At home, at weekends or whatever, it wells up and I can't handle it. "But most of the time I can just about handle it, you sort of have to get through the day."
The acrimonious Beatles split sparked a damaging and lengthy court case and left bad feeling between the four members. Lennon's song "How Can You Sleep?" on Imagine, released in 1971, was widely assumed to be blistering attack on his former songwriting partner.
But by 1974, Lennon was in the midst of the so-called "Lost Weekend", in fact many months of heavy drinking and drug abuse in Los Angeles during a separation from wife Yoko Ono.
The dates fit, too, in that until 1974 international borders and their respective drugs convictions had kept Lennon and McCartney apart. Lennon was unable to travel to and from the United States because he was under a deportation order, while McCartney only gained a United States visa that year and travelled to Tennessee with his band Wings in June.
Sir Paul said he played drums, one of his early specialities, on the run-through of 1950s rock and roll classics including Midnight Special. Other songs might have been Matchbox and Lucille, he said.
"It was a strange session. The main thing that I recall, apart from the fact that Stevie Wonder was there, is that someone said `What songs shall we do?' and John said: `Anything before '63 I don't know anything after '63!' Which I understood, because the songs from your formative years are the ones that you tend to use to jam. I ended up on drums for some reason."
Revelation of the session is bound to spark an international hunt for the tape, which could be worth millions of pounds.
"No, I don't have a tape of it," Sir Paul said.
His assistant Geoff Baker believed Sir Paul would also have sung during the jamming session.
"Obviously Sir Paul has known about it all along, but sometimes if you ask the right question you get the right answer," he said.
Sir Paul has talked more frequently and comfortably about the past recently, since work on the Anthologies. They saw the release of "new" Beatles singles "Free As A Bird" and "Real Love" featuring Lennon's voice from archive demos and the instrumentation of the three surviving Beatles.
His latest solo album "Flaming Pie," currently number two in the charts, takes its title from some typically surreal writing by John Lennon in a 1961 article for Mersey Beat.
Beatles experts said it is believed it was the first time Sir Paul has spoken of the 1974 session, although it has been documented by others in the past. Some "bootleg" illicit releases from the session are in circulation.
Rock journalist Paul Du Noyer, whose biography of Lennon's solo career We All Shine On was recently published, said: "Lennon's girlfriend at the time May Pang described the session in her book The Lost Weekend. Paul and Linda turned up unexpectedly one evening and they decided to have a jam. The only thing anyone can ever remember playing is Midnight Special which has been out on a bootleg."
Du Noyer, a founding journalist on Q and Mojo magazines, did not doubt that the precious tape had a notional value of millions. But he added controversially: "It is probably complete rubbish and I think it would be better left unfound."
The feud between McCartney and Lennon had often been misrepresented, he felt.
"I think that although they `hated' each other professionally they still had a personal regard, and occasionally they did spend time with each other. But they only met on literally a handful of occasions in the 1970s. It would always be Paul that initiated these meetings rather than John -- John was much less sentimental about the Beatles."
Self-confessed Beatles fanatic Chris Shaw from Tunbridge Wells said he had a prized bootleg recording of Lucille which purported to be from the sessions.
"It's absolutely abysmal," he said cheerfully. "John's obviously out of his head on something or other."
The exchange between Lennon and McCartney about "Something from before '63" could be clearly heard at the beginning, he said.
Stevie Wonder, songwriter Harry Nilsson and Linda McCartney were also supposed to play on the tape, he said.© Copyright 1997, Vintage Rock