One of my first musical memories is of being given a Beatles wig. They sold them in Woolworths but it wasn’t a normal wig with individual strands of hair – it was vacuum-formed plastic and felt like wearing a crash helmet. When it was on you looked like you had Paul’s hair, but when you took it off you were left with what looked like a scar on your forehead.

The Beatles were big in my house but it was the lovable moptop Beatles, the London Palladium Beatles. Once they’d grown their hair and become hippie-ish, my family were always a bit down on them. I remember taking a shoebox and transforming it into a miniature replica of the set of Ready, Steady, Go, the television music show that was like a precursor to Top of the Pops. I cut off the front, drew little exit signs and cut out little Beatles. Looking back, that was when I started using music to create these little worlds.

I’m not a very experienced songwriter but I read that John Lennon would sometimes think: “I want to do something like Roy Orbison.” They would quite openly copy genres. So a song like Sweet Illusion, on my new album, is definitely me having a go at a 60s song.

Another influence you may hear is Frank Sinatra, who my parents also listened to. They didn’t have a big record collection. In fact they never seemed to buy records, so I’ve no idea where these ones came from, but they had a couple of Sinatra albums. After a few drinks everyone in the family would join in singing That’s Life. I didn’t realise it until later because my parents were in the ice cream business and we lived in a tenement, but my family were actually very musical. My father played piano, my uncle played guitar, another uncle played accordion and another uncle sang and did comedy bits. So when they got together at family dos they were a band, and everyone would tear into it. My uncle’s guitar was more like a piece of furniture than an instrument – it had huge strings that you needed big Italian peasant hands to play, but he battered the hell out of it and it sounded great.

I was very lucky not to get into drama school. They said “you’re awful don’t come here” – quite rightfully at the time – so I went to art school instead. It was great. We all turned up dressed like Neil Young circa After the Gold Rush, wearing long hair and cheesecloth shirts. Then, during my first summer there, the Sex Pistols exploded and everyone came back in plastic trousers with cheaply dyed hair. Suddenly there was this ethos that you could be in a band, so I got involved with that. Mine were called the Dream Boys. Our influences were Bowie, Talking Heads and the Cramps, who were like a voodoo-swamp version of the Munsters. For some reason, that seemed like the direction to go in. Perhaps not very wisely.

This was around 1977, and back then you could take a tape to a venue and get a gig. The art school had a very staid student body that looked after entertainment. They tended to bring in hippie bands, jazz acts and George Melly. We wanted more aggressive music, so we ended up providing it ourselves. But our shows weren’t full of people spitting. There was quite a schism between London and the rest of the country – I think the people of Glasgow frowned on all the spitting and that kind of nonsense.

We always struggled with drummers. It was like Spinal Tap – some drummer or other would come and sit in for us. Then, one night at a place called the Rock Garden, I asked if anyone knew a drummer who wanted to join our band. A 17 year old in the audience asked if he could have a go and, rather grandly, we said we would audition him – as if we had any idea what we were doing. He turned out to be a brilliant drummer and he was very funny too – you’ll know him now as the comedian and US talkshow host Craig Ferguson.

It all goes back to that shoebox. At the time I thought I just loved showing off but really what I loved was being able to create a whole world on stage and presenting our ideas to people. We kept at it. We tried and tried but we weren’t getting anywhere. Eventually you run out of steam because you have no money and you’re eating Pot Noodles on Christmas Day. It seemed like everybody else in Glasgow was getting signed or doing a Peel Session and we weren’t. I would get the coach down to London and go round all the record labels but nothing ever happened.

Still, all the local bands were very sweet to us and offered us support slots. We supported Altered Images a few times and their singer Clare Grogan had just done the film Gregory’s Girl. One night the director Bill Forsyth was in the audience, and after the gig he invited me to be in his film Local Hero. If someone standing backstage at a sweaty gig tells you they’re making a film in Scotland, you assume it’s going to be a 16mm, half-hour thing without a script. But it turned out to be a proper film. It felt like fate was pushing me towards acting and away from music, so I embraced that.

To be honest, I’d never been that interested in writing songs. And I was never the guy at the party who brought out the guitar. But I became friendly with Dr Robert of the Blow Monkeys and he is that guy at the party with the guitar. He’s a living jukebox, a fantastic singer and player. He would invite me to play along with him, and then he challenged me to write my own material.

I wrote the songs for my debut album St Christopher while I was filming The Suicide Squad in 2019. I had so much downtime on set that I thought I’d spend it writing and see what happened. A lot of it was rubbish but some of it was OK. I love the Kinks and live in Muswell Hill so we booked their studio Konk to record it all. But then the pandemic hit and we couldn’t go. Instead we took the GarageBand demos and sent them off to people. Then they would come back with a great sax player on or whatever.

There are not many people who release their debut album at the age of 62, but that’s the great thing about technology: anybody can do it. When I was originally trying to be in the music business you had to be signed to Sony or RCA to release something, but now you just need a computer.

I wasn’t nervous of putting this music out. It doesn’t matter. It’s not my profession. My friends who are musicians have had extreme ups and downs and maintained their commitment to music through all of that. My cousin’s son is Lewis Capaldi and he’s a case in point of someone who has dedicated his life to music. His dad was driving him around Leith and Aberdeen – anywhere with a pub he could stand in with a guitar and sing – because he had to do it. I actually appeared in his video for Someone You Loved – which was the song of his that exploded, so I was delighted to be in it. He’s fantastic, but he’s in an entirely different league from me. My songs were originally more something I was doing for myself. I thought, OK, if I am going to have a go at making music it has to be music I want to make. I’m not going to do a Peter Capaldi Christmas album. It couldn’t be Malcolm Tucker sings Sinatra: “Have yourself a merry fucking Christmas.”

My new album Sweet Illusions is really my way of picking up where I left off 40 years ago as an art school student. It reminds me of Glasgow in 1984, when there were a lot of synths and fuzzy guitars, lots of echo and reverb, and lots of dreamers whose dreams were being crushed. The city has a noir-ish quality to it, a bit like Liverpool and Manchester do. It’s the Victorian city centres and the rain and the night and all that. Very cinematic. You can conjure up images and stories.

A lot of the songs deal with aging. Wondering where all the time has gone. Big Guy is about those people who were once full of braggadocio and swagger but are now dribbling on their jumpers. We remember them as something else now.

The single Bin Night is a lullaby. I’m a grandparent now so suddenly I have babies and lullabies in my life again. It’s wonderful, but being Scottish there’s always a melancholic streak in me that will seek out the bleak thing about it. In this case it’s the ticking clock. These fabulous children bring all this vigour and chaos into your life, but how long do you have left to spend with them? That made me think of the entropy of the universe and how awful the world is. And how just about the only moment I have any control over is putting the bins out. I don’t know if it’s the only song ever written about bin night but it’s a great subject.

• Peter Capaldi’s Sweet Illusions is available now on Last Night from Glasgow records