James Murphy throws a miniature invisible basketball and feigns a bratty fit of frustration when it bundles off the board and out of touch. “See? I'll never be a basketball player. I just don't have the presence of mind for it,” he says, shaking his head, that mischievous grin lurking out from beyond his beard. Murphy is many things to many people: frontman to now defunct electro icons LCD Soundsystem, label boss to the influential DFA Records, producer, DJ, coffee entrepreneur, watch manufacturer, comedian, budding novelist and now with the release of Shut Up and Play The Hits, a two hour document of his band's final show at Madison Square Garden, a film star. I've asked him, with so many strings already to his bow, is there anything he can't do?

“The thing about basketball is that I can't shoot or dribble. Two pretty critical skills in that sport. Oh and I'm not a great dancer, either,” he continues. “I'm not purposefully or consciously prolific or anything. I just like creating things.” His latest creation, the brilliant, twisting Shut Up is a mere hour away from its British premiere at the Hackney Picturehouse. It's here we meet, while the crowds begin to drift in. There's every bit the colour and vibrancy you'd expect of a film premiere, the air heavy with chatter and the crunch of flashbulbs as celebrities ghost by on the red carpet, but it feels a little like a wake, like the fans filing into the cinema auditorium are here to pay their last respects to an act whose kind don't come around too often.

LCD Soundsystem began in 2001 in Murphy's native New York, where their upbeat party anthems in a way became synonymous with the city's defiance in the years that followed September 11. The wide spread of sounds on their 2005 self-titled debut (“recorded by me on my own, then made into a live thing,” remembers Murphy) meant there was something for everyone – its bouncing rhythms propped up by a brash, punk undercurrent, with Murphy musing eloquently in the most inviting of pop bellows at its epicentre. It was the beginning of a band with a rare ability to move both on the dancefloor and somewhere more profound. That Shut Up's crowd scenes are punctuated by glimpses of fans in floods of tears is telling of the emotional punch of Murphy's songs, and the distress felt that he's leaving them all behind.

“It was tough but felt like the right thing to do,” he says of the decision to break up the band. Having kept busy with various collaborations and projects since, before launching back into his LCD guise to promote this film, has the enormity of that decision still to hit him? “You know, at the moment it comes over me in waves. You forget about it and then it comes back around. It's like death. You get on with your life then one day, it's Christmas or whatever, a birthday and it comes back. Things hit you at different times for different reasons.” There's a pause before he laughs. “I'm sorry, this is very morbid all of a sudden. It's the Irish in me. What I mean to say is, this movie felt an interesting way to celebrate the end of that chapter.”

Interesting is an understatement. In an inspired spin on the traditional concert movie, Shut Up melds footage of that final show at Madison Square Garden in April with reality-bending scenes of Murphy as he prepares for the show and life without the commitment that has dictated his every move for the past decade, loosely scripted in a manner befitting his semi-improvised stage manner (“I just made [the lyrics] up every time and had notes to help me go down the right path,” he recently told a reporter. “Each performance was different. The words caught on record just happened to be the words I sang that day.”) It's a film that reaches beyond music to something more human, both celebrating and agonizing over the prospect of renewal with brilliant lyricism – in one scene, Murphy speaks to Klosterman about life after LCD as a camera captures him shaving his beard.

“We originally wanted to make an entirely fictional film with some real things. We were going to play a concert and there was going to be the interview with Chuck Klosterman, which would be a real interview, but there was also going to be dream sequences and all sorts of weird shit and we weren't even going to show the band play,” explains Murphy. “We had the same ideas about wanting it to not be a stupid concert movie with big cranes. It seemed like this great opportunity.”

Much like his music, the 42-year-old is easy to love but near impossible to pin down. “I'd say my mantra is to not be the sort of guy whose worldview can be boiled down to a single mantra,” he says, flashing me another grin. “I'm not a good boiler-downer. I'm a bigger-upper, an expander, not a contractor. Have you heard me ramble on?” I notice he has come dressed tonight in the same attire he wears onscreen – dishevelled suit, loosened tie, white trainers – and begin to wonder if there's a character Murphy feels tied into playing as the LCD Soundsystem's talisman, one he's tired of assuming.

Perhaps the most memorable flashpoint from Shut Up comes early on, as Klosterman posits Murphy with a theory: People, the journalist suggests, are remembered for a series of successes but defined by their single biggest failure. What is Murphy's defining failure? The singer answers sombrely that it could well be breaking up LCD Soundsystem. Is that a genuine concern or was he playing up to the cameras? “It's not a concern, it's just a fact,” he tells me. “I'm not worried about, else I wouldn't have done it but sometimes, you never know... I regret it in little ways. Not regret it, actually, but I miss it. No regrets. None.”

You hear stories. The astronaut who returns to Earth overawed with what he saw, distant and resenting. The Olympic gold medal athlete who, as the cheers of the crowd fade, falls into depression. Shut Up and Play The Hits so easily could have basked in a band at their pinnacle, but instead asks the more searching question: when the house lights go up and the euphoria ends, where now? How do you start again? Such is James Murphy's warmth and spirit – on record and in person – that it's easy to be troubled by the uncertainty and darkness that simmers under his documentary. But as we part, he beams me a parting smile that tells me he'll survive in a world without LCD Soundsystem. The question is – will we?

Shut Up and Play the Hits in cinemas now. For more info on exclusive items to preorder, as well as the DVD and Blu-ray, out 8th October, go to: shutupandplaythehits.com

Find Al Horner on Twitter: @al_horner.