The anecdote ends with Macca rinsing the dishes under a tap in the kitchen, prompting a “private moment” for Hay. He pauses. “‘Stone me,’ I thought, ‘Paul McCartney’s doing my dishes.'”

Live, Hay is not just a talented singer-songwriter but a skilled raconteur. Ask him what audiences can expect in Edinburgh and Glasgow this week, and he responds drily: “They should expect nothing, then whatever happens will be well beyond their expectations.”

Thirty years ago, Kilwinning-born Hay was one of the biggest stars in the world. He’d relocated with his family to Melbourne while a teenager and, later, put together Men at Work. With him as lead vocalist, the band had a string of substantial hits including Who Can It Be Now?, Down Under, Overkill and It’s a Mistake. They won a Grammy award, and sold an estimated 30 million albums.

Since the band’s break-up in 1985, Hay, who is 60 at the end of June, has put together a solid solo career and 11 albums. His latest, Gathering Mercury, was assembled over some four months in Los Angeles, where he now lives.

“It’s my strongest record to date,” he says. “I felt like I made this album with my old man. He was a great singer and dancer, and had poetic flair. He just never followed that path. Even if I didn’t want to think about the fact that he was gone, he was present in his absence. Living in Los Angeles,” he adds, “I also have access to beautiful musicians, who made it pretty special for me.”

The “old man” is his father Jim, who died a few years ago but was an important figure in Hay’s life. There’s a remarkably poignant song on the album, called Dear Father, with the line: “I never got to say goodbye/I was singing on the River Clyde/ and I didn’t know.”

It turns out that Hay was playing the Renfrew Ferry, some 20 streets from where Hay senior was born. As he has said: “There’s some kind of bleak poetry in that – very bleak.” Saturday night’s show will be the first time he has played Glasgow since then.

“I don’t have a definitive belief in an afterlife, but I do feel like I had his help when I was working on this album, especially alone late at night in the studio.”

Hay is currently in the middle of an extensive tour – Australia during February and March, the US this month, Europe the next, and back to the States. Is playing live, meeting his fans, what keeps him engaged?

“It’s simply necessary, for all kinds of reasons,” he says. “You have to ask yourself what you want to do after breakfast, an important question to answer. I choose to go downstairs and write tunes, record them, then go out and play them live for people. An old-fashioned approach perhaps, but nourishing nonetheless.”

He has spoken fondly of his time as frontman with Men at Work, saying in a recent interview: “They were high times. I felt like Superman. We won big time. It doesn’t really get any bigger than what happened to Men at Work in terms of success.”

He has worked hard to get his name back out there after the demise of the band. Was it difficult at first?

“It’s still not without its difficulties,” he says, “but it’s far outweighed by the fact that I gather new audiences, and they are growing in a pure, organic fashion, devoid of pesticides.”

Live, Hay has a lot of solo material to choose from, but he cannot forget the hits that made him famous. “I use my hit songs from the Men At Work days as a condiment,” is how he puts it. “You could say I lightly pepper the show with hits.”

He has a good life now – a home and studio in Topanga Canyon (he’s married to Peruvian singer Cecilia Noel), and regular visits back to Melbourne. His own, single-artist label, Lazy Eye Records, allows him to own and control his recordings.

We associate Topanga Canyon with songwriters such as Neil Young. Is there a vibe there that is conducive to creative types? “Yes,” says Hay, “there’s no danger of singer/songwriters becoming extinct in Topanga.”

Colin Hay plays The Caves, Edinburgh, on Friday and Glasgow’s O2 ABC on Saturday.