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The romantic comedy, written by and starring Sean of the Dead star Nick, follows reluctant dancer Bruce as he steps back into the world of salsa to win the heart of the beautiful Julia (Rashida Jones).
"I've known Olivia for a long while," Nick told HELLO! "We're really good friends and I love working with her because she's an amazing actress.
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"Rashida, we were meant to meet the first time for half an hour, and that became three and a half hours. We just laughed. I saw in her someone who understood."
BAFTA winner Olivia Colman plays Bruce's sister Sam in the raucous comedy, and says working with close friend Nick on such a light-hearted film was joy after her recent more serious roles.
"It was a no brainer really," said Broadchurch star Olivia. "It's those people and you get to learn to dance. It's so much fun. We had a ball doing it. I got slightly obsessed with it."
"Later on I think everyone might be trying it out again," she joked. "I might end up with a broken nose! The high kick and the lots-of-spins was someone else, but everything else was me. The floor sweeps – that was me!"
Los Angeles-born Rashida, 37, plays charming boss Julia and was immediately drawn to the role.
"It's a sweet tale about overcoming your fear as an adult, and doing something that you don't necessarily think you're good at," she told HELLO! "But you're passionate about it, so who cares what anyone else thinks?
"This cast is a dream team," she added, praising her co-stars. "Nick and Olivia… Olivia is such a huge star in this country now, but in the States people have not caught on to her brilliance. Chris is a comic genius. It's really a stellar cast."
Despite the praise he has received, Nick told HELLO! he initially had reservations about making a film centre on dancing.
"I was a dancing fan but I wasn't a fan of people watching me dance," he said. "There's a weird look that people give to a big lump who's dancing well. I thought, 'I don’t want that'."
At a press screening of the film in January, Nick told audiences he had struggled to dance even at his own wedding to production executive Christina.
"I'd always wanted to do a dance film, but it was like a dirty little secret, and eventually one night after enough beer it came out in an email [to his producer], because I think secretly I wanted to get caught!"
Christina was in London to support her husband at the premiere, as was best friend and collaborator Simon Pegg – who cameos in the film during an epic dance-off between Nick and Chris O'Dowd – and Chris' wife, presenter Dawn O'Porter.
"I love to dance, but I'm more of a freestyler than a salsero," joked Chris. "I tried to incorporate a little salsa into our wedding dance. I think people will fall in love with dancing watching this film."
Cuban Fury hits cinemas on 14 February