OK, so I'm sitting in Noel Harrison's front room and he's strumming his beautiful, handmade, Mark Whitebook acoustic guitar (other owners of this rare rosewood beauty have included James Taylor and George Harrison) and then he begins to sing the signature song that turned him into a legend: Windmills Of Your Mind.

It is, of course, the hauntingly beautiful title track of the 1968 Steve McQueen/Faye Dunaway movie The Thomas Crown Affair, a song so sublime it won the 1968 Oscar for best original song in a film.

There are candles burning and glasses of wine on the old pine chest that passes for a coffee table. We have shared a perfect omelette (unsalted, good butter – that's the secret) which he rustled up in his kitchen, and as he sings, visions of kaftans, cheese-cloths and flares waft before my eyes, as I am transported back to the era of tinkling bells, flower-power, gentle peace and communal love. Man, life as a features interviewer doesn't get much better than this.

We are meeting because, at the age of 77, Noel has been asked to play at this year's Glastonbury Festival, on the "Spirit of '71" stage. It's his first time at Glastonbury, and he's thrilled to have been invited to play.

When we meet at his home in Devon, he's still frantically trying to decide what to include on his set list – besides Windmills, of course, which is a bit of a given. Apparently, he's planning to sing it in both English and French ("Les moulins de mon cœur") and there will also be a beautiful string quartet arrangement.

He's an inspired choice, actually, because if anyone should be able to capture the essence of that flower-power era, it's Noel, who, in the early Seventies, having tired of a Hollywood celebrity lifestyle that had seen his first marriage crumble, turned his back on all the "ego-inflating bullshit" and took off across America in a Chevy station wagon plus tent trailer, in search of a quieter, simpler life.

He had moved to the States from England with his first wife Sara in the mid-1960s, and quickly became "hot" in Hollywood.

He starred in a TV series (Girl from UNCLE) with Stefanie Powers, and had various top 40 hits.

For a while, he had the house, the pool, the stables, the celebrity lifestyle … until it all came crashing down.

Sara took off for England, taking their three children with her, while Noel took off for Nova Scotia with Maggie, who would become his second wife. Thousands of hippies in that free-wheeling, free-loving age "tuned in and dropped out", and Noel was no exception. Inspired by the hippy cult classic book Living the Good Life, by Helen and Scott Nearing, they built their own house and went "back to the land", eschewing electricity and growing fruit and vegetables.

It was, he admits, a rather naïve, pre-Aids, "sexual revolution" era, but beautiful for all that. And it's that sense of innocence that he wants to re-capture at Glastonbury.

"I'm very honoured to be asked to do the festival," says Noel. "I only hope I can live up to it. There definitely will be a sense of the older generation passing on the flame to the younger one. I want to evoke the sense of idealism that led me to take off in the Chevy, trying to seek out a simpler life. I'd like to pass it on in what I sing and play."

Noel will be joined on stage by his good friends Phil Rossiter (lead guitar), Bill Birks (drummer and bass), and Will Harrison (percussion), his 39-year-old son from his second marriage, who is travelling over from the States.

"Will's a gifted musician," says Noel. "He's got a band called The Last Star Pilot, and they're going to be roving ambassadors for the Spirit of '71 stage." And, he adds, with a twinkle, that "Will was conceived in that year, in Maine – so he's the living embodiment of the spirit of '71!"

Will's twin sister Chloe, who lives near Totnes with her husband Julian and children Dylan and Jasper, will also be there, cheering them on.

It was eight years ago that Noel returned to live in Britain, after some 40 years in the States. He brought with him his American third wife, Lori, his partner of 23 years.

They initially had come over to help out Noel's step-daughter, Zoe, who ran a cyber cafe in Ashburton. "She wanted to go to Australia, to see her first grandchild, so Lori and I came over from Los Angeles and ran the cafe for her for two months. But Lori absolutely fell in love with it here, so ... we came over for good."

And it works out brilliantly, because there are many members of Noel's family living close by – and family is important to him.

Noel himself is, of course, the son of legendary actor Sir Rex Harrison, who won an Oscar for his role as Professor Henry Higgins in the 1964 film My Fair Lady, co-starring Audrey Hepburn. Sir Rex also famously talked to the animals in the massively popular 1967 film, Doctor Dolittle.

Noel and his father were not close when he was little. Sir Rex's son from the first of his six marriages, to Collette Thomas, Noel's parents divorced when he was six. But the war was on, so he went to live with his mother's parents in Bude, North Cornwall.

He was sent to private schools, eventually ending up at Radley, in Abingdon, Oxfordshire. Then, when he was 16, his mother – by now living in Klosters in Switzerland having fallen in love with a ski instructor – made him an offer. "She said, 'Would you like to stay at Radley and try and get a scholarship to Oxbridge, or would you like to come and live with me and try and get into the British ski team?'" No prizes for guessing what Noel chose. By 1953 he was British ski champion; he also competed at two Olympic Games, in Oslo and Italy.

Noel finally became close to his father in his mid-twenties, when Sir Rex's third wife, Kay Kendall, was dying. "When I was in Switzerland, for a while he was in St Moritz with Kay, and it was then that I really got closest to him, when Kay was very ill. He took me into his confidence, and it was very nice to be able to help."

Later, Noel would go on theatre tours in America, doing productions of some of his father's musicals, such as My Fair Lady. Did his father mind? "Well, when the twins were born, I got an offer to do My Fair Lady for a large amount of money, and I really needed it at the time," he says. "So I went to see my dad in New York, and I said, look, I've really steered away from this as much as possible, but now I really need the money, so how do you feel about it? And he said, Oh, why not? Everyone else is doing it!"

Today, Noel is well known around the ancient Devon stannary town he has made his home. Watch out for him in the supermarket, buying butter for his omelettes, or catch him playing his guitar and singing in village halls around Devon, where he's patron of local arts organisation, Villages In Action ("I love doing that, the audiences are lovely, so sweet and kind, they seem to like my stuff").

He also performs and helps out with local amateur dramatic groups, often alongside members of his family – several of his five children and grandchildren live nearby, such as his actress eldest daughter Cathryn, 52, who is married to retired oil company executive Paul Laing.

"Cathryn's so brave," sighs Noel. "She had a freak accident last summer, after she did a local amateur dramatic production of Macbeth at St Lawrence Church, here in Ashburton. She stepped onto a pavement and fell awkwardly and broke her leg. She was in a wheelchair to start with, but now is able to walk with a crutch."

Cathryn's sister Harriet, a former showjumper, also lives nearby, with her two children, Lucas and Toby. "Harriet lives up in Holne, near her mother, Sara," says Noel. "She's an equestrienne, and still does a lot with horses, but she had a bad accident several years ago, otherwise she'd have been in the Olympics."

Noel's son, Simon, who will be 50 in November, is the third child from his marriage to Sara. A psychologist, he is married to Philip, a theatre set designer. "They had a wonderful wedding, although I scolded them for wearing identical suits," says Noel. "They're such a happy couple, so sweet – an example to us all."

All Noel's wives, past and present get along, apparently. "I'm a very, very lucky man in that sense," he says. "And, believe it or not, they all like me, in spite of my sometimes dolt-like behaviour in the past."

When he sings locally, Noel likes to do two 40-minute sets, working his way through songs that map out his life.

He loves playing country and folk music, and also enjoys playing with his friend Phil Rossiter who has a Zydeco band in Exeter.

It's all a way long from the days when Noel stood on a huge sound stage at Paramount Studios in Hollywood alongside a full orchestra and sang Marilyn and Alan Bergman's famous lyrics, set to Michel Legrand's soaring string arrangement, with Legrand himself conducting.

Round like a circle in a spiral;

Like a wheel within a wheel;

Never ending or beginning;

On an ever-spinning reel...

"I'm afraid that, for me, recording Windmills wasn't a very significant moment," he shrugs, as he returns his guitar gently to its stand. "It was just a job that I got paid $500 for, no big deal. Norman Jewison, the director of The Thomas Crown Affair, liked my voice and picked me to sing his film's title track. The composer, Michel Legrand, came to my home and helped me learn it, then we went into the studio and recorded it, and I thought no more about it!"

He smiles, remembering. "It's an amazing song, I don't get tired of it at all. It's almost like a meditation quality, the images keep shifting," he adds.

Sadly, it was not Noel who sang Windmills at the glittering Oscars ceremony in Hollywood all those years ago – that honour fell to Jose Feliciano, much to Noel's annoyance, as he was making a film in England at the time, and unable to get away.

However, this year, when the beautiful opening notes of Windmills are played on the Glastonbury stage, it will definitely be Noel singing the song. Surrounded by his family, maybe he'll feel that his own wheels have finally come full circle.