Twelve Years a Slave, directed by British filmmaker and former artist Steve McQueen, took the biggest prize, best picture, at the Los Angeles ceremony.
British film Gravity, starring George Clooney and Sandra Bullock, won seven awards, including best director for Mexican-born UK resident Alfonso Cuaron and the visual effects prize for its London team.
Twelve Years a Slave took three Academy Awards, including best supporting actress for tearful newcomer Lupita Nyong'o, who told the audience: "It doesn't escape me for one moment that so much joy in my life is thanks to so much pain in someone else's."
Backstage, she said she felt "a little dazed", adding: "This is my first time here and I feel like Willy Wonka in the chocolate factory."
McQueen made history as the first black filmmaker/producer to collect the statuette for best picture and dedicated his award to victims of slavery.
He said: "Everyone deserves not just to survive but to live. This is most important legacy of Solomon Northup. I dedicate this award to all the people who have endured slavery and 21 million people who still suffer slavery today".
The filmmaker jumped for joy on the stage but later joked he was actually "as cool as a cucumber".
He said backstage: "Everyone saw me jump but truly I am so ecstatic. I'm so happy for us all. It's one of those moments in life that might never happen again but you're living it, you're there and it might never happen again so emotions just take over."
He said the film's success was proof times had changed.
He added: "It's the mark of development and how we see that time in history now, the background characters are now in the foreground, their history and lives are being recognised in a way more than ever before. People are ready for this narrative. Before it was quite painful, but now people want to look at that history."
Brad Pitt, who helped produce the film, praised McQueen while Prime Minister David Cameron tweeted his congratulations.
Best actor went to former romantic comedy star Matthew McConaughey for Dallas Buyers Club, while Cate Blanchett took home best actress for her role in Woody Allen's Blue Jasmine.
Blanchett, who beat Bullock, Dame Judi Dench, Amy Adams and Meryl Streep, said films with strong female characters were not niche, adding: "Audiences want to see them and in fact they earn money. The world is round, people."
British film was also celebrated in the award for best documentary short which went to The Lady in Number 6: Music Saved My Life. It came a week after its inspiration, pianist and world's oldest Holocaust survivor, Alice Herz-Sommer, 110, died in London.
Director Malcolm Clarke, who lives in Canada but learned his trade at the BBC and ITV, dedicated the win to her "extraordinary capacity for joy and her amazing capacity for forgiveness".
The technical expertise of the UK film industry was recognised when Gravity picked up awards for sound mixing and sound editing, while the movie also won cinematography, original score and film editing. Original score was won by Steven Price, a musician from Nottingham, who thanked his family, joking: "Mum, dad, Jenny, sorry I made so much noise while I was growing up."
McConaughey's Dallas Buyers Club co-star Jared Leto won best supporting actor for his role as an HIV-positive transgender woman and dedicated his win to the "36 million people who have lost the battle to Aids" .
The best song went to Let It Go from Frozen. Steve Coogan failed to win the best adapted screenplay Oscar for Philomena, with 12 Years A Slave writer John Ridley picking up the prize. The award for best original screenplay went to Spike Jonze for Her.
Host Ellen DeGeneres opened the awards with a string of jokes poking fun at the event, before starring in selfies with stars and even ordering pizzas.