That summer, with child-friendly single “Mary Had A Little Lamb” gambolling around the Top 30, Wings upgraded from a van to a bus, and toured Europe. Denny Seiwell: “It was an open-top London double-decker bus. They’d painted it bright colours and fitted it with mattresses on the top deck for sunbathing. It only went 35mph, that was the problem. In Germany we were late and they sent five BMWs to meet us on the motorway.”

Incredibly, Wings’ third single, “Hi Hi Hi”, received another Radio 1 ban – this time for sexual innuendo. However, an incident on the European tour would have much more serious repercussions than any BBC embargo. In Gothenburg, Sweden, the McCartneys and Seiwell were arrested and fined for possessing marijuana. Media reports of the bust triggered a second bust at the McCartneys’ farm by Scottish police. Paul now found he was repeatedly denied a US visa. The drug convictions also kept him out of Japan, one of rock’s most lucrative markets.

Seiwell: “That wasn’t just a menial fine that was paid in Gothenburg. That cost him a lot of money.”

Paul and Linda McCartney are sauntering down a dark, unlit road one evening in September 1973, tape recorders and cameras in hand, the red Lagos mud underfoot. Paul, who has chosen Nigeria from a list of EMI’s studios round the world, has multiple duties on his plate – including playing lead guitar and drums on the new album. McCullough and Seiwell, unhappy that their retainers did not increase in line with recent chart success (“My Love”, “Live And Let Die”), have quit – Seiwell by telephone, hours before the Lagos flight –reducing Wings to an overstretched trio. A car passes the McCartneys on the road, and stops. An African man gets out. Paul tells Linda he thinks they’re being offered a lift.

In his Soho Square office 34 years later, McCartney’s face creases up. He is relishing this story. It has already become the interview’s centrepiece anecdote. “They told us at the studio not to go walking late at night, because there was crime and stuff. We just went (sarcastically) ‘Yeah, sure!’ We were hippies. We thought we were immortal.”

The McCartneys have now caught up with the car. Paul gives the man a friendly nod.

“I said, ‘You know what, this is so nice of you – but it’s a beautiful evening and we don’t want a lift.’ I’m bundling him back into the car. ‘Come on, now. Get in the car. Get back in that bloody car.’ I’m doing the Liverpool thing. ‘You’re not giving us a lift. Go on, mate, off you go!’”

He decides to illustrate what he means. Getting up from his chaise longue, he grabs me by the shoulders and tries to push me off my chair. He’s quite a lot stronger than you think.

“So then the car stopped again. Only this time it stopped a bit more sharply – and suddenly all the doors flew open, bam bam bam, and five or six of them jumped out. The little one had a knife. Now the penny drops, finally.”

The McCartneys were stripped of their pricey cameras and tape recorders, and returned to their rented house deeply shaken. Next day, recounting the story at the studio, they were told they would probably have been killed if they’d been a black couple. The robbers had left them alive as they wouldn’t expect white people to identify them.

“Looking back on it, it was funny,” McCartney says, shaking his head helplessly. “I’ve got this – I think it’s basically stupidity. I must admit there’s an element of stupidity there. When I look at these things afterwards, I think, ‘What are you on?’ But I see it as a sort of enthusiastic innocence. It’s enthusiasm to me. Yeah, let’s do this. Don’t worry about that. Everything’ll be great!”

Following the mugging, Wings’ Nigerian adventure turned thoroughly sour. Local musicians came to the studio to intimidate them. Paul suffered a bronchial condition that made him fear he was having a heart attack. Yet the driven McCartney slaved over Band On The Run in Nigeria and London like no Wings project before, and the result was a career landmark. The songs were saturated in infectious hooks. The arrangements were witty and inspired. Band On The Run followed its patchy predecessor, Red Rose Speedway, to No 1 in America, and became Britain’s best-selling album of 1974. The unqualified triumph did wonders for McCartney’s self-confidence. He was back. He’d made a classic. Even John Lennon said so.

And as McCartney now overtook Lennon to become the most successful and critically acclaimed ex-Beatle (ironically the two men had a rapprochement in New York at this time), the image of Wings changed totally. Once a good-time band for blokes and birds, they increasingly catered for a more exclusive, high-end clientele. Dustin Hoffman hung out with them. The Magnificent Seven’s James Coburn was among the startled celebrities on the amusing sleeve of Band On The Run. Wings joined the jet set. By 1976, once McCartney had finally been granted a US visa, there would be $80,000 end-of-tour parties in Hollywood mansions, attended by A-listers Warren Beatty and Tony Curtis. Wings, the band that had played Little Richard covers for 50p on-the-door at Nottingham University, were now grossing $5 million for seven weeks’ work.

The mid-’70s were Wings’ commercial heyday. The albums Venus And Mars (1975) and Wings At The Speed Of Sound (1976), while sorely flawed, dovetailed consummately with the baby boomers’ insatiable appetite for easy-going arena-rock (Eagles, Peter Frampton, Steve Miller) both at home and abroad. Back to full strength after the addition of Jimmy McCulloch (guitar) and Joe English (drums), Wings racked up a fifth consecutive US No 1 album in 1977 (with the triple-live Wings Over America), having obliterated the indoor world audience record (67,100) in Seattle on the tour in question.

Of course, by late 1977 in Britain, there were new forces to compete with. McCartney, never so foolish as to try to identify publicly with the punk scene, instead trusted his judgment and released a misty-eyed waltz, composed in tribute to the area of Scotland where he lived. While the Sex Pistols sneered at stupid old EMI on an album released that month, McCartney and his record company savoured their colossal international hit. Statistically outrageous, “Mull Of Kintyre” sold over two million in Britain alone.

“We were expecting it to be a flop,” McCartney protests. “We thought we should really be putting out something thrashy, fast and loud. But it had occurred to me that there weren’t any new Scottish songs. I like the pipes, you know. The skin-tingling, bloodcurdling thing. So we released it, thinking ‘Nah… it’s not the time for it.’ But I remember ringing here [his office] and the guy said, ‘It’s selling 30,000 a day.’ As a joke I said, ‘Don’t get back to me until it’s selling 100,000 a day.’ And the next week, it was.”

He laughs, and goes on to tell a story – which may or may not be true – about him and Linda being stuck in traffic in the West End when “Mull Of Kintyre” was enjoying one of its nine weeks at No 1. Through the car window, they espied a large gang of punks loitering on the pavement.

“They looked pretty menacing,” he says, rolling his shoulders like Del-Boy in Only Fools And Horses, “and there were a lot of them. I said to Linda, ‘Keep your head down. Get the sunshields [in the car] down..’ And of course one of them recognises me. [Cockney accent] ‘Oi, Paul! Awright, Paul!’ I thought, oh no… The guy’s going like this [signalling for Macca to wind down the window]. So I put the window down a little bit. And he says: ‘You know that “Mull Of Kintyre”? It’s faaking great!’ I thought, ‘Now that is cool. Punks like it.’”

With its buttery production and soft-rock electric pianos, Wings’ 1978 LP, London Town, doubtless kept those punks thrilled. It had partly been recorded on a yacht moored in the Virgin Islands, where Wings relaxed with cordon bleu dinners and water-skiing sessions. So it was a surprise when McCartney unveiled a new Wings line-up that year, featuring two newcomers who looked like members of Blondie. Producer Chris Thomas, fresh from Never Mind The Bollocks, was brought in, and McCartney promised a “raw” Wings sound.