Mick Fleetwood and I are taking tea in a stylish hotel overlooking London’s Hyde Park. We are talking about his father Mike, who died in 1978 aged 62. Suddenly, Mick spots something out of the window.

“See the horses?” he says, looking out of the window and leaping out of his chair to point them out to me.

“It’s so cool, talking about Daddy and there he is!” Knowing the somewhat colourful background of Fleetwood and his eponymous band (past issues with cocaine and alcohol, for example), you could be forgiven for thinking the drummer had flipped.

But no. What we are looking at is the Household Cavalry crossing the park in the autumn sunshine, breastplates gleaming.

“He was a Royal Horse Guard and he used to make that same ride. Mummy (his mother Biddy, now 97) used to sit in the building that’s now the Mandarin Oriental Hotel over there when she was a young woman,” he points, “and she watched those men on the horses crossing the park and she ended up being with my dad. So cool.”

Fleetwood, now 67, is obviously still in awe of his late father, who ended up buying himself out of the Army, and joining the RAF for the duration of the Second World War. The pair were remarkably close; certainly closer than you would usually expect an upright Air Force man and his academically ungifted musician son to be, and it is to Mike’s sense of leadership and understanding of personality that Mick attributes the fact that he has been the father figure of his band Fleetwood Mac through 47 years of personnel changes, musical differences, illnesses and romances.

Throughout it all, as well as keeping time for the supergroup, he has kept the band together. He has now written a second autobiography, Play On, about his life. This is still entwined with the Mac, who are currently on a world tour coming to Britain in May, rejoined by songwriter and keyboard player Christine McVie after a break from the band of a mere 16 years.

Mike and Biddy already had two daughters when Mick came along, and were not the 1950s parents you would expect. “None of us had conventional careers,” remembers Mick. “My parents knew that none of us were destined for cookie-cutter jobs. They already had a blueprint with Sally (who became a sculptor and clothes designer) and they sent her off to art school. Then Susan wanted to be an actress and then they had this little lad who wasn’t getting anything from school, so they let me go off and live in London with Sally and pursue a music career.”

Mike Fleetwood was the sort of chap they do not make any more; a self-made man from Liverpool who travelled to Germany before the war, witnessing gatherings that would see Adolf Hitler rise to power; becoming a soldier and then an airman and then, before entering the world of Civvy Street and bringing up a family, pursuing a career as a writer.

“Dad was not all the huff and puff of the RAF; there was this dreamy, poetic thing there for sure. It was the perfect template for me. He had an attitude of ‘as long as something gets done, it doesn’t matter who gets the kudos. That serves no purpose other than to say me, me, me’.”

Mick’s parents wanted their children to pursue their own passions

Fleetwood Mac are arguably one of the most interesting mega-bands. From a blues outfit at the start, with John McVie still in the band which bears his and Mick’s names, Bob Brunning and the extraordinary guitarist Peter Green, the band has gone through several incarnations until arriving at the current, classic line up of Fleetwood, McVie, Stevie Nicks, Lindsey Buckingham and Christine McVie.

The band are back together again for a new album and tour, and Fleetwood is clearly delighted. He draws a large circle in the air, and says: “It is, as I say on stage, the completing of a circle. Christine returning to the band; well, that was a door that was never closed, and that has always been the better choice for me.

“I don’t write people off and I would much rather leave the door open than push people away, no matter what has happened. I would rather prefer to work at being liked than to be cynically truthful with people all the time and closing the door in their face.”

I’m amazed when Fleetwood says that he has never really thought about the band as one where men and women are on an equal footing as performers and songwriters; one of what I think is the band’s strengths. “I’ve never been that Superman creature, all huff and puff, and making a delineation between us. My parents and my sisters were the perfect template of being in touch with your feminine side. And it’s fun.”

Being Mick Fleetwood, it has to be said, does look like more fun than several barrelfuls of monkeys, despite the aforementioned brushes with substances that were doing him no good, and a bankruptcy. Now living on the Hawaiian island of Maui, where his mum Biddy also lives, he exudes rangy elegance, with a dress sense also influenced by his father.

“He always loved clothes; the military makes you learn to turn out, and at my boarding school you learned to turn out. If you don’t spit and polish your shoes, or press your shorts at night under the mattress, you’d be in trouble.”

Today, he looks every tall, slim, tanned, Bohemian rock star dresser, in white skinny jeans, a mango-coloured shirt worn under a buttery-soft light brown suede waistcoat. Fleetwood admits that he loves shopping, but it wasn’t so easy as a teenager, despite living in cool Notting Hill.

‘Being gangly and tall and having no money was a huge problem, so when I came to London, I started dressing myself like so many others, from secondhand stores, with Liberty fabric jackets, jeans, all that kind of stuff that actually fit. I loathed shirt sleeves as they were always too short; I ended up looking like David Byrne from Talking Heads in Stop Making Sense!”

Being a tall teenager has been a bizarre help in Fleetwood’s showbiz career. “Being six foot six, thin as a beanpole, probably looking quite odd –‘Is that a boy or a girl?’,” he mimics, in the way our parents baffled generation did. “And you’re walking around Notting Hill Gate in blue jeans, with a pair of wooden balls hanging from your belt and hair down to your bottom, you get used to being looked at for being different.”