Bjorn Ulvaeus, the second-hairiest member of Abba, has agreed to grant The Sunday Times an interview on one condition: we serve him lunch. Not buy him lunch; a songwriter worth $300 million by some estimates hardly needs a freebie. But to physically bring him food and put it down in front of him.

So here I am, nervously hurrying over to Ulvaeus’s table, in waiter’s waistcoat and pinny, bearing taramasalata, tzatziki, roasted red pepper hummus and a selection of olives. We’re in Nikos’s taverna on the Greek island of Skopelos. Except we’re not really. We’re actually in London’s O2 arena, in a theme-park version of a Greek taverna. There are ferry timetables and Nana Mouskouri posters on the walls. The set designers have exhausted Britain’s entire stock of plastic bougainvillea.

The original production of Mamma Mia! The Party in Stockholm.

This is the extremely camp setting for Mamma Mia! The Party, co-written by Ulvaeus. In essence, it is a highly immersive dinner-show, where you’re not sure who’s a real waiter and who’s a West End veteran about to burst into song beside your table.

Mamma Mia! The Party is a highly interactive dinner-show.

If you’ve seen the Meryl Streep films or the original stage show, you’ll know what to expect: a tortured plot whose main aim is to cue up renditions of Abba’s greatest hits. Only this time you get a four-course Greek meal. Tickets start at $186; drinks and merchandise are extra.

A Swedish version has been sold out in Stockholm since January 2016. “I never expected that,” says Ulvaeus, as he reaches into a basket of homemade bread. “Then again, I thought that Mamma Mia! would run for a year in a small theatre in London.”

The plan was always to bring The Party to Britain. Ulvaeus lived in Henley-on-Thames for most of the 1980s, and Abba’s big breakthrough came in Brighton, in 1974, when Waterloo won the Eurovision song contest for Sweden. “Despite the fact that the UK gave us zero points!” he cackles, thumping the table. “Look it up!” (I did: our judging panel, to its eternal shame, gave a maximum five points to Italy’s Gigliola Cinquetti singing Si.)

Mamma Mia! The Party will play to 500 people, up to eight times a week. That’s a lot of lamb kleftiko. Rhubarb, the show’s caterer, has hired only waiting staff who have “pizzazz”, says Jan Kraemer, its general manager, a German by way of Lanzarote.

The waiters go through a week of training that includes improvisation and synchronised dance as well as the usual stuff involving food hygiene and how not to drop plates on the floor.

Ulvaeus wants me to see what it takes to be a pretend Greek taverna waiter. I have about 20 minutes before my VIP lunch guest arrives.

Improvisation and synchronised dance as well as the usual stuff involving food hygiene and how not to drop plates on the floor.

Kraemer takes me through the basics: stay in character, get strangers talking to one another, keep the body language open, and don’t mess up the drinks orders. If I get the job (I won’t), the enjoyment of 25 guests will depend largely on my competence. “Sound easy?” asks Kraemer. It doesn’t.

Luckily, Ulvaeus is a game judge of my waiting talents. He slips into impressions of the most awkward dining guests from his favourite sitcom, Fawlty Towers, as I present him with a Greek salad and “charred octopus with ouzo and wild oregano dressing”.

Is he worried that British audiences on a big night out won’t behave as well as those strait-laced Swedes? “We’re very much alike, you know, Swedes and the Brits, in that respect,” he says. “I didn’t expect the Swedes to get up and dance like they do. I think they’re going to be roughly the same. Maybe a bit more raucous here.”

Bjorn Ulvaeus in the Nikos Taverna, the setting for Mamma Mia! The Party.

My tableside manner seems to be working its magic. Ulvaeus is opening up and shooting the breeze. Does the king of Eurovision think about Brexit much? “You bet! I think about it every bloody day. It was a symbol of Britain not wanting to belong to this Europe that I feel I belong to. I was shocked and I was sad, but I’ve come to terms with it. I just hope we don’t have to fill in those bloody landing cards again.”

Next he spills the beans about his love life. Ulvaeus has been married to Lena Kallersjo, a Swedish music journalist, for 38 years. Before that, more famously, he was one half of one of the two sexiest marriages in pop. He and Agnetha Faltskog divorced in 1980. Their bandmates, Benny Andersson, Ulvaeus’s songwriting partner, and Anni-Frid “Frida” Lyngstad, divorced the following year.

He was one half of one of the two sexiest marriages in pop.

“[Agnetha and I] grew slowly, slowly apart and decided, amicably, to go our separate ways. And we did,” says Ulvaeus. “I was a bit sad in the beginning, but it was so clear that this is what it had to be. Clear for her and clear for me.”

Ike and Tina Turner they weren’t. “It was probably the best divorce anyone has had.”

All four members of Abba attended the Stockholm premiere of Mamma Mia! The Party. Will they be appearing at the O2 as well? “I’m pretty sure Benny will be here,” he says. “But about the two ladies, I think they’ll decide at the last moment.”

There is, I regret to report, no Abba members WhatsApp group.

However, all is not lost for fans who still dream of a sequin-encrusted reunion. Two bona fide new Abba songs have been recorded, and Ulvaeus promises we will finally hear them next year. In what he says will be a “big spectacular”, they will be performed, alongside old songs, by “Abbatars” — digital copies of the band members being developed by a company in Silicon Valley.

The years have been kind to Ulvaeus, 74, and his bandmates. (Both Agnetha and Frida are now “the blonde one”.) Nevertheless, the Abbatars will be based on the band in their 1979-80 pomp. After lunch, he’s off to a top-secret meeting about his virtual self.

“Abbatars” are digital copies of the band members developed by a company in Silicon Valley.

Ulvaeus is very happy with his London Party. “It’s all there now,” he coos. “When it really works, it’s almost like a ballet.”

He recently built a hotel in Vastervik, the coastal town in which he grew up, and his youngest daughter, Anna, is running it. Next, he’s taking The Party to Las Vegas and Hamburg. The Abba empire is still growing 38 years after the band called it a day.

There’s downtime occasionally. Ulvaeus reads the papers: he subscribes to The New York Times, The Washington Post, The Financial Times and — good man — The Times and The Sunday Times. He has eight grandchildren, aged between four months and 18 years. He kayaks around the Stockholm archipelago, which explains the tanned, toned arms.

Overall, Ulvaeus emanates the healthy, good-humoured contentment of somebody who knows he has written some of the greatest pop songs committed to vinyl.

“In our view, they were perfect. Not that they were perfect songs, but every part of them was the way it should be,” he says. “We never let go of a song until we knew this was the absolute best we could do.”

He didn’t leave a tip.