Jeff Goldblum has huge hands. I know this because we are finger to finger at the keyboard of a Steinway grand piano in a glitzy central London hotel lobby, and he easily outspans my meaty paws. We are working our way through Herbie Hancock’s classic jazz tune Cantaloupe Island, the myriad heavy silver rings on his long fingers flashing under the lights as he takes a solo. If you want to get properly up close and personal with someone, play a piano duet with them. He hums the tune under his breath and rocks his shoulders into me as he plays. When it’s my turn to solo, he somehow manages to wrap his broad, 6ft 4in leather-jacketed frame around me to throw in some bass stabs down the bottom of the keyboard. He grins and laughs. Jeff Goldblum is in the room. And he’s enjoying himself.

No wonder. Goldblum the film star, the one who misplaced his mantra in Woody Allen’s Annie Hall, who gave us all nightmares as he gene-spliced himself with an insect in David Cronenberg’s The Fly and battled aliens in Independence Day, is about to release his first jazz piano album, and he can’t quite believe his luck. “I’m grateful for the whole damn thing,” he tells me.

Our duet took place following an hour’s conversation at another keyboard tucked away in a bar, off the lobby of the Corinthia Hotel in London. Goldblum says he knows this instrument, a clunky electronic piano tackily set into the bar. “I’ve played it before. When I’m on the road I go early in the morning to a local jazz club or a piano like this and I run through my stuff.” He plays his way through 40 key jazz standards to keep them up to scratch. He’s done it for years. “At 5.30 this morning I was in the lobby playing on that lovely Steinway. I am nothing if not disciplined.”

At 5.30 this morning I was out there in the lobby playing on the lovely Steinway

That’s the point. Through all the films, the huge grossers like Jurassic Park and Thor: Ragnarok, the cult classics like The Big Chill or Earth Girls Are Easy, through three marriages and his 65 years, playing jazz piano has been the constant. “I purposefully kept it under the radar,” he says. “I always wanted to be an actor. But playing the piano, that was never a career. I was doing it for fun and the joy of it and, you know, seeing how far it goes.”

In October last year, Goldblum appeared on The Graham Norton Show plugging his scene-stealing part in Thor: Ragnarok as a hedonistic, manipulative Master of the Universe; to be fair, Goldblum’s rarely met a scene he couldn’t thieve. “The producers for Graham Norton called and said Gregory Porter, who I think is great, was to be the musical guest. Would I like to accompany him? And I said, ‘Very much, yes I would.’”

For many viewers, who didn’t know that Goldblum is a musician with his own ensemble and weekly LA club date, the moment came as a surprise. It is, to be fair, not the most comfortable of performances. Goldblum is stooped over the piano and leaning into the sheet music like it’s an exam he thinks he might fail, though he relaxes a little as he slips into a solo full of flurries and tight corners. “I was reading the hell out of that piece,” he says now. “I’d really only done it a couple of times.”

Tom Lewis, head of A&R at Decca Records in London, watched the show. “I think somewhere in my peripheral memory I was aware Jeff played, but the trigger really was that performance.” He later flew to Los Angeles, took in one of Goldblum’s shows at the Rockwell club with his ensemble, the Mildred Snitzer Orchestra – named after a friend of his late mother’s in Pittsburgh – and signed him for an album. “I was really impressed. He’s very accomplished, but he’s also exceedingly respectful to other musicians,” Lewis says. “What he’s really good at is being a band leader. There’s a little bit of the Count Basie swagger to him.”

‘What kind of peevish nincompoop would I be if I wasn’t satisfied?’: Jeff Goldblum and Jay Rayner. Photograph: Pål Hansen/The Observer

The result, recorded live with an audience at the legendary Capitol Studios, is a blast. There’s no doubting its jazz credentials. For a start it’s produced by Larry Klein, who has worked with Herbie Hancock and Joni Mitchell. It kicks off with Cantaloupe Island and finishes with Duke Ellington’s Caravan. There’s a haunting trumpet solo by the world-class German trumpeter Till Brönner on It Never Entered My Mind, but also huge crowd pleasers.

Imelda May gives a brilliantly gravelly rendition of Nat King Cole’s Straighten Up and Fly Right; there’s a blissful take on Nina Simone’s My Baby Just Cares for Me with vocals by Haley Reinhart, and Goldblum duets and flirts with Sarah Silverman on Me and My Shadow. “We’re not asking to be compared to contemporary virtuosos,” Goldblum says of the recording. “We’re not trying to impress anybody. We’re just saying, ‘Have a listen to this and see if you like it.’”

The result is indeed very likable. For the most part he’s not the star soloist, just the pianist in a cracking outfit. Compared with the myriad albums by other actors and comedians attempting to prove they’ve got soul by over-stretching their mediocre musical skills, it’s that rare creature: an un-vanity project. And the man can really play. I suggest it’s odd that, after 30 years of shows in the US, he should end up being signed by an A&R man from London. “Yes,” he says. “It’s random. It’s magical.”

Jeff Goldblum grew up in Pittsburgh with three siblings, a mother who had worked in radio, a doctor father and a Steinway grand piano. “It was just there,” he says, when I express surprise at such an illustrious instrument. “I think it was an investment.” Both his parents loved music and theatre and insisted the kids took dance and music lessons. Goldblum was a poor classical student. “I had some co-ordination, but no discipline and I dreaded the lessons because I hadn’t touched the piano all week.”

So what changed? What was the tune he learned that made him realise there was another way? All of us who turn to jazz piano have one of those: a tune that sends us down a new road. “Oh, oh,” he says, in that perfect Goldblum half stutter, the sound of an idea coming to him faster than his mouth can handle. “It was called Ally Cat.” He plays me the first few bars of something caught between ragtime and barrelhouse, full of stride piano left-hand chords, his long fingers flicking this way and that. “I went, ‘Wait a minute, wait a minute…’” – he is playing the part of himself when young. “I don’t care how long it takes me to play like that. It’s what I want to play.”

‘Even though my parents were conventional in many ways, they had a love of music’: Jeff Goldblum. Photograph: Pål Hansen/The Observer

He began reading his way through chord sheets for tunes from the Great American Songbook, songs like Stairway to the Stars, Deep Purple and Misty; and paid close attention to Pittsburgh’s own jazz piano star, Erroll Garner. “I’m not really sure how I learned about playing chords, but somehow I did.” As with everything on planet Goldblum, he makes it sound effortless. At 14, he grabbed a phone book and called local bars explaining he’d heard they were looking for a pianist. It was a lie; he didn’t even know whether they had a piano. Unsurprisingly most of them didn’t have a vacancy, but a couple booked him. Well of course they did.

Remarkably, his parents drove him to the gigs. He makes it sound like a reasonable thing for a parent to do with their 14-year-old son. “Even though my parents were conventional in many ways, they had a love of music. They would check out the bar, make sure it was OK and leave me to it.”

But acting was still the career of choice. At 17 he moved to New York, bought an upright piano for his apartment and took acting lessons from a renowned coach, Sanford Meisner. His approach, Goldblum says, was also useful for his development as a musician. “He taught me that acting is interactive. You come to life out of your presence with the other actors, by listening. I come from the era of ensemble acting, all those Robert Altman films.” To play with other musicians you also have to listen. The problem was that he had never played with anyone else.

That changed through working with the actor Peter Weller (who would eventually make his name in RoboCop) on the film Buckaroo Banzai. Weller plays trumpet and had been encouraged by sometime clarinet player Woody Allen to start performing. “Peter Weller suggested we do something and I knew a guitarist so we started playing at this brunch place on Sunset Boulevard.” That was 30 years ago. Weller has moved on but the music hasn’t stopped. “Now every week when I’m in town we get together and play.” Only when they were offered bigger gigs at festivals and the Hollywood Bowl did they finally settle on a name. “Apparently we needed one.” Dear old Mildred Snitzer was accorded her moment in the sun, for an “orchestra” that rarely goes beyond seven or eight members.

‘Oh sure, I like to sing, I like to do it all’: Goldblum performs with the Mildred Snitzer Orchestra in Pasadena in 2017. Photograph: Rich Fury/Getty Images

I ask him to play me something, and he goes into the lovely Jules Styne and Sammy Cahn tune I Fall in Love Too Easily. Despite the limitations of the instrument we’re on – the amplified sound comes out of a speaker behind us, which is just plain odd for a piano – his version is soft and lyrical. He throws in a vocal at the end. Does he like singing? “Oh sure, I like to sing. I like to do all of it.” Until relatively recently his weekly shows were, he says, random events. “I’d bring fake books” – volumes of chord sheets for well-known tunes – “and start flicking through and get the audience to tell me to stop and whatever it was we’d play. I like to cold read.” A few years ago one of his band members told him that he ought to talk to the audience more. “And I thought he was right so I started going out 30 minutes before and playing word games with the audience.”

You can find grainy video snippets of those shows online. What’s most striking is just how completely Jeff Goldblum he is. It’s the same today here in the bar. He is exceptionally comfortable in his own tall, imposing skin. For such a star, he’s brilliant at the tricky business of being himself. He is a superb Jeff Goldblum, the Jeff Goldblum you want him to be – intense, amused, interested – and yet he manages it without being smug or overbearing.

When it came to recording the album, that presented challenges. “Larry Klein came to see the show at the Rockwell and he immediately said that if we put Jeff in a sterile studio, it wouldn’t work,” says Tom Lewis from Decca. “We had a choice. For the sake of the record do you take microphones to the Rockwell or do you take the Rockwell into the studio?” They went for the latter, importing the whole club into Capitol Studios, where Sinatra and Nat King Cole recorded.

Next Klein turned to the tunes. “Larry said, ‘What’s your identity?’” says Goldblum. “So we settled on the 1950s/60s Blue Note stuff.” Originally this included a lot of difficult material by Thelonious Monk, which he plays through to me. “Do you know this one? Or this one? Or this?” I admit I don’t. They’re tricky tunes. Clearly Klein decided the listener might feel the same way, because none of them made the cut.

Goldblum admits the process has changed him as a piano player. “It’s made me focus on what I’m doing.” He is now taking lessons from fellow band members. I ask if he regrets not having spent time on these basics when he was much younger. “Oh no. No, no, no. That’s how it worked out for me. Maybe if I’d burdened myself, I wouldn’t be having as much fun as I am now. I’m kind of a late bloomer.”

In 2014 Goldblum, previously married to the actors Patricia Gaul and Geena Davis, married the former Canadian Olympic gymnast Emilie Livingston, who now works in film. (She doubled for Emma Stone for the aerial dance scenes in La La Land.) “We’ve had two babies. I could have thought: ‘I wish I’d done that before’, but it happened when it happened. I like to say I’m right on schedule.

“My approach to music has bled into my acting and it’s nourished it. I’m looser and deeper. I’m liberated in some way. I can be more effective.” That said, there is a fundamental difference. “Acting can grip you with identity issues. What’s this going to lead to? If I fail, what’s that going to mean?” And the music? “I don’t need anything to come from this. I’m happy to have done it and who the heck knows who will buy it? Decca would probably like people to buy it.” The band will tour. There will be shows in London, Paris and Berlin. It means he gets to play.

“I’m not an observant Jew,” he says. “But we have a saying: Dayenu, which kind of means if nothing else would happen, I’d be entirely satisfied. What sort of peevish nincompoop would I be if I wasn’t satisfied? It’s an embarrassment of riches.”

We fool around at the piano together for a while. We try out Sweet Georgia Brown. He shows me Erroll Garner’s Misty. We talk nerdily about chord voicings and diminished scales. He has a musician’s openness; every conversation at a keyboard is an opportunity to learn something new. Finally, we’re told we can get on the Steinway in the lobby, where they’re serving afternoon tea. Together we advance on the young woman hired to entertain the guests with a bit of French classical. She looks up, slightly startled. I say, “This is Jeff Goldblum.” She nods slowly, as if I’ve stated the obvious. She says, “Would you like to play…?” Goldblum fixes her with one of his fabulous grins, eyes wide behind his thick-framed glasses. “Well thank you. I would like that very much.” Would Jeff Goldblum like to play the piano? Well of course he would.

Jeff Goldblum and the Mildred Snitzer Orchestra: The Capitol Studios Sessions is released on 9 November. The orchestra plays two shows at Cadogan Hall in London as part of the EFG London Jazz festival on 17 November