If Georgie Fame ever gets round to writing his autobiography, it'll be an eventful one.

There's the story of how the teenage mill worker from Lancashire went off in search of lucrative employment in the music business, wound up stuck in London with no money and, within a few weeks, found himself on the Spring 1960 tour that was to be the last the world saw of rock'n'roll star Eddie Cochran, of Summertime Blues and C'Mon Everybody fame.

Fast forward to the 1970s and a nervous Fame is knocking on the door of the house in California that songwriting legend Hoagy Carmichael called home, seeking – and getting – Carmichael's blessing for an album of his songs that Fame and Glasgow-born jazz singer Annie Ross have borrowed the required money to produce.

And on top of those stories there's his 1960s pop stardom, the mainstream television success in partnership with Alan Price, being thrown onto the scrapheap by the music business in the 1970s, pursuing his love of jazz through an album and tours with Count Basie, recording with another hero, Mose Allison, and countless gigs as the man Van Morrison and Bill Wyman came to rely on – Wyman still does – as their musical director.

This, in truth, only scratches the surface and as he celebrates his 70th birthday year, Fame is still adding to the experiences and, as he puts it, continuing the musical education that began formally when the then Clive Powell's dance band-playing father sent him to piano lessons at the age of seven. The formal bit didn't last long and Fame was gigging as soon as he could.

"I've always considered myself a working musician," he says. "I had my successes and I had a real low point for a couple of years in the 1970s, but I was always prepared to get on the band bus or whatever, and go out and graft to put food on the table."

Touring with Cochran was, he says, a fantastic experience for a 16-year-old piano player who had been given the name Georgie Fame by pop impresario Larry Parnes, whose stable of stars all had names such as Billy Fury and Marty Wilde.

"I was backing up Gene Vincent on that tour, and I remember when we played the Caird Hall in Dundee, the audience invaded the stage and got rock'n'roll banned in that venue for a few years," he says. "Gene was great but Eddie was amazing. I always credit him with introducing Ray Charles to the great British public because as well as his hits, he sang Ray's What I'd Say and Hallelujah I Love Her So. He had a great repertoire and he was a really good guitar player, which doesn't always get acknowledged."

From the Larry Parnes stable of backing musicians, Billy Fury took four players and called them the Blue Flames. Then when they had a falling out, Fury was ditched and Fame, by now having discovered the magic of the Hammond organ, led the band, working their socks off on multiple gigs per night and Soho all-nighters and landing hit singles Yeh Yeh, Getaway and The Ballad Of Bonnie And Clyde.

By the time Fame fell out of favour with the pop business in the 1970s, he'd already prepared for a move into jazz by working with the Count Basie Orchestra – he has fond memories of their Glasgow Empire appearance in the late 1960s – and it tickles him that he has managed to make a success, on both sides of the Atlantic, with the music that's routinely seen as non-commercial.

"I always listened to jazz and its influence was in my style somewhere," he explains. "The Blue Flames in the beginning were jazz musicians and they still are. I still have my bigger band, with Guy Barker on trumpet, Alan Skidmore on tenor, Anthony Kerr on vibes and Alec Dankworth on bass, although it's the family trio that I'm bringing to Glasgow Jazz Festival."

Working with his sons, Tristan and James, on guitar and drums respectively is a great thrill for Fame, even though he warned them not to follow him into music and paid for private educations so they could go on to university and get proper jobs.

"I'm very proud of my boys," he says. "I told them: music's great fun and you can always go out and enjoy yourselves playing it but don't expect it to put food on the table. But they didn't want to go to university and 25 years later, here we still are. It's more rhythm and blues we do than jazz, and I'm firing on five cylinders, if you like, with two hands on the Hammond keyboard, my left foot on the bass pedals, the right on the swell pedal and a microphone at my throat. But I love it.

"Performing music means you're sharing emotions whoever you're playing with, and we don't burst into tears or anything, but playing with your family takes it into another dimension."

George Fame's Three Line Whip plays the Old Fruitmarket, Glasgow, on Saturday.