It was a contest between two wildly different films – a 3D space disaster movie and an unflinching portrayal of 19th-century American slavery – and on paper it was the former, Gravity, which emerged as the biggest winner at the 2014 Bafta ceremony.

It won six awards, including best director and best British film. But 12 Years a Slave unquestionably picked up the biggest prize, best film, with Chiwetel Ejiofor named as best actor.

In a year when no one film swept the board, American Hustle also came away with three prizes.

Alfonso Cuarón was named best director and said you would not know it from his accent but he considered himself a part of the British film industry. He has lived in London for 13 years and joked: "I make a very good case for curbing immigration."

The film, with a Mexican director, American stars and an outer space setting, raised a few eyebrows when it was included in the best British film category. Nevertheless, it fulfilled the rules and duly won.

Gravity's haul was impressive, only one short of the seven Baftas won by The Artist in 2012 and The King's Speech in 2011. The record of nine, held by Butch Cassidy and the Sundance Kid, was never in jeopardy.

Its British producer, David Heyman, said winning was "beyond belief" and paid tribute to the UK company behind the amazing special effects, Framestore, which brought applause from the audience. Those effects got their own award, best special visual effects, beating a shortlist that also included The Hobbit: the Desolation of Smaug, Iron Man 3, Pacific Rim and Star Trek Into Darkness.

The film also won for best sound, best cinematography and best original music, the latter by British composer Steven Price. He thanked his "mum and dad for having such a great record collection when I was a kid".

Accepting the best film award, 12 Years a Slave director Steve McQueen said: "There are 21 million people in slavery now as we sit here. I just hope that 150 years from now our ambivalence will not allow another film-maker to make this film."

Ejiofor beat fellow shortlisted actors Bruce Dern, Christian Bale, Leonardo DiCaprio and Tom Hanks. He thanked McQueen for "your work, artistry and passion in this project". Addressing him he said: "This is yours, I know that … you know that. I'm going to keep it, that's the kind of guy I am, but it's yours."

Ejiofor was visibly moved and a little nervous. Few people will be surprised if the London-born actor is not having to do it all again at next month's Oscars ceremony.

Cate Blanchett was named best actress for the Woody Allen film Blue Jasmine and she dedicated the award to the late Philip Seymour Hoffman. "You raised the bar and all we can do in your absence is to continue raising it." She added: "Phil, buddy, this is for you, you bastard, I hope you're proud."

Some of the evening's biggest cheers came as newcomer Barkhad Abdi was named best supporting actor for his portrayal of a Somali pirate in Captain Phillips.

He triumphed in an extremely strong category which included Michael Fassbender, Bradley Cooper, Matt Damon and Daniel Bruhl. Abdi thanked his co-star Tom Hanks and the director Paul Greengrass "for believing in me before I believed in myself." Abdi was a limousine driver in Minneapolis, which has a large Somali community, when he turned up on a whim at an open audition and was cast.

Baz Luhrmann's The Great Gatsby picked up two awards with Catherine Martin and Beverley Dunn winning best production design and Martin by herself winning best costume design. Martin thanked her team of 300 who worked on the film but, mercifully, not individually.

Rush, the dramatisation of Niki Lauda and James Hunt's Formula 1 rivalry, won the best editing award although the editors Dan Hanley and Mike Hill could not be there because director Ron Howard said they were busy editing his next movie. "I think they'd thank the hell out of me," he joked.

American Hustle, David O Russell's 1970s grifting caper, won three awards. Jennifer Lawrence was named best supporting actress, and fittingly for a film with so many alarming haircuts and sideburns, it also triumphed in the best make-up and hair section. Its director, Russell, and Eric Warren Singer were the recipients of the best original screenplay award.

Steve Coogan and Jeff Pope were the surprise winners in the best adapted screenplay section, beating John Ridley who wrote 12 Years a Slave. Coogan said he was inspired to adapt the book, The Lost Child of Philomena Lee by Martin Sixsmith, after he read an article in the Guardian four years ago. There were many thanks although Coogan said there were still another 60,000 women who had not traced their children, taken from them by nuns and put up for adoption, and "their story isn't yet over".

The sometimes controversial and always distinctive director Peter Greenaway, whose films include The Cook, The Thief, The Wife and Her Lover and The Pillow Book, received an outstanding British contribution to cinema award.

Greenaway, never shy in coming forward – in 2002 he accused film-makers of killing cinema with cynicism and laziness – follows in the footsteps of directors such as Ken Loach, Mike Leigh, Derek Jarman and Alan Parker. He said he was "very, very surprised" to get the award and regarded it as "an encouragement for the continual reinvention of cinema".

Dame Helen Mirren was given Bafta's highest accolade, a fellowship. Somewhat appropriately, since she has portrayed the real Queen on both film and stage, it was given to her by a member of the royal family in the shape of Prince William. Giving her the fellowship the prince joked: "I should probably call her granny."

In her acceptance speech Mirren paid tribute to a teacher who inspired her and all teachers who inspire, asking people to applaud. She quoted from The Tempest: "We are such stuff as dreams are made on and our little life is rounded with a sleep," she said. "My little life is rounded with this honour."

The only award voted on by the public, the EE Rising Star award, went to Will Poulter who first came to attention as Lee Carter in the 2007 film Son of Rambow and last year stood out in the comedy We're the Millers.

The film not in the English language award went to Paolo Sorrentino's The Great Beauty.

The outstanding British debut award was presented by Steve Coogan to Kieran Evans, the writer and director of Kelly + Victor, a Liverpool-set love story.

Other winners included a harrowing film examining the Indonesian death-squads of the mid-sixties. The Act of Killing won in the documentary section and its director Joshua Oppenheimer used his speech to accuse Britain and the US of actively supporting the 1965 genocide in Indonesia and the regime which followed.

The best animated film went to Disney's Frozen, also one of the most successful. It has grossed nearly $1bn worldwide and beat Despicable Me 2 and Monsters University to the Bafta.

The winner in the best short film category was Room 8 and Sleeping with the Fishes won in the best short animation section.

The awards, a dry run for next month's Oscars, attracted many big Hollywood names including DiCaprio and Brad Pitt, and for the first time in years guests arrived on the red carpet under a fading blue sky.

The ceremony was once again amiably and wittily hosted by Stephen Fry who declared himself "humbled, honoured and in the best sense of the word, paid to be here."

The evening went smoothly and there were was precious little gushing and rambling from award givers and recipients although there were a few grimaces at some of Fry's attempts to hurry things along.

"Please don't kiss and dry hump everyone when you win," he said, "just leap on the stage like a bloody gazelle."