Gary Barlow gets Abba’s Agnetha Faltskog singing

But the first time Barlow landed in Stockholm, Agnetha didn’t turn up to meet him because she was on holiday. The second time he made the effort to travel from London he was assured that Agnetha was back from (another) holiday. “But,” the 42-year-old recalls, “she wasn’t feeling very well. So on both occasions I missed her.”

Luckily however, the songstress has broken her self-imposed exile to promote the album, simply called A, and in the past couple of months has gone from elusive pop legend to ubiquitous pop star. It’s a snowy day in Stockholm, and here she is, sitting in front of me, demure but twinkly, poised and polite, offering me coffee and cake. Agnetha-from-Abba, in the radiant, appropriately wrinkled flesh.

“I thought it was maybe too... snobby,” she smiles, “but then I got used to the title. And I thought, why not? It’s my name, and it’s the first A in Abba.”

The album project began after she was approached by two Swedish writer/ producers – they had written songs with her in mind on spec. She was sufficiently enthused to pause her gentle, semi-retired regimen of dog walking on her island home and spending time with her three grandchildren, and return to the recording studio.

“I also have been written about like I’m very mysterious. I try every time to explain that I’m so normal. I’m not Garbo! I would rather be... who shall I say?”

Lady Gaga?

“No! No way! No, I’m just a normal Swedish woman.”

She’s not, of course. To millions – and millions – of fans around the

world, she is the radiant heart of Abba. Yes, she shared the microphone duties with Anni-Frid Lyndgstad (Frida), their voices working in exquisite tandem to bring to life the words and music of Benny Andersson and Bjorn Ulvaeus. She was a soprano, Frida mezzo-soprano, “and that’s why the harmonies worked so well,” she explains. But it was Agnetha who shone brightest. And not just because of the jumpsuits.

Abba’s golden years began with victory in Brighton at the 1974 Eurovision Song Contest with Waterloo, and ended in 1982 with a broadcast of Happy New Year live from a Stockholm studio to the London set of Noel Edmonds’ Late, Late Breakfast Show.

In that frenetic time the couples in the band (Agnetha and Bjorn, Frida and Benny) toured the world, split up, wrote songs about it (The Winner Takes It All), and kept working. Agnetha and Bjorn also had two children – in 1973 and 1977.

They only ever cancelled two shows. Once was when Frida had a “bad cold”. The other came after a “terrible flying experience. It was never an accident,” Agnetha says with a visible shudder, “but it could have been”. During a flight from Boston to New York, foul weather meant two failed attempts at landing. The pilot touched down on the third go, with the fuel perilously low. “That was terrible. I had a shock, and still had to work after that.

“And that I think is the bad thing with this work,” nods Agentha. “You can never be ill. You have to work anyway. You have to fight. But it’s the same with actors and theatre people – you don’t want to cancel, you want to stay there all the time.”

In her 1997 memoir, As I Am: Abba Before & Beyond, Agnetha writes of those shows that they demonstrated “a thin line between ecstatic celebration and menace”. Given that she never enjoyed performing much in the first place – even as a pre-Abba teenage solo star in Sweden – playing to baying thousands and being chased to airports must have been particularly gruelling for the shy girl from the small town of Jonkoping.

Her post-Abba life, notably the case of an obsessive Dutch fan who relocated close to her home, can’t have helped. Is she thrilled enough with the album to perform it live?

“No, I can’t!” she laughs, lightly but at the same time firmly. She recently “performed” with the other members of the band, recording voiceover contributions for the recently opened Abba the Museum in Stockholm. And last month she took to the stage at the G-A-Y nightclub in London, basking in the ecstatic applause of the audience as the DJ played Dancing Queen. But that, it seems, is as far as she’ll go. “That’s my weakest [thing], the live thing. And also the fact that I’m older now, so I can’t do that. I don’t want to disappoint people.”

So is she glad that Andersson and Ulvaeus have already publically declared their lack of interest in a reported $1 billion payday for an Abba reunion?

“Oh yes!” beams the quietly sparkling legend. “We said no because they wanted 250 shows or something, it was incredible. No chance! No chance,” repeats Agnetha, calmly. “We had done it.”

In the end, Gary Barlow did encounter his heroine when she travelled to London last month. “I was very excited to meet her. But we were being filmed at the same time,” he notes wryly (the footage will be seen in the BBC1 documentary Agnetha: Abba and After). “So on the one hand it was a little bit uncomfortable. But on the other, she was just a total joy – so gracious and lovely. So the meeting went great.

And we just ended up chatting for about an hour in the end. It was really, really nice. And to hear Agnetha sing again...” Barlow marvels, “you just can’t help but have your spine tingled by that voice.”

ABBA v TAKE THAT

Studio albums

Abba: Eight (five reached number one in the UK)

Take That: Six (five got to number one in the UK)

Singles released

Abba: 73

Take That: 30

UK number ones

Abba: Nine

Take That: 11

UK bestselling albums

Abba: Gold: Greatest Hits has sold 5,100,000 to date (the second bestselling album ever in the UK)

Take That: Progress sold 2,800,000 copies by 2011 (it sold 235,000 copies across the UK on the first day of rlease, making it the fastest-selling record of the century)

Concert dates played around the world

Abba: 112 The last two performances of their 1977 European tour were at the Albert Hall, where the box-office received 3.5 million ticket requests – enough to fill the venue 580 times.

Take That: 289 The final eight nights of the 2011 Progress Tour at Wembley Stadium set the record for the highest-grossing residency (£38m).

See Agnetha: Abba and After tonight 10:35pm, BBC2