The Bafta for best film has been awarded to Richard Linklater's film Boyhood.
The Bafta for leading actress has been awarded to Julianne Moore for her role in Still Alice.
During her acceptance speech Moore thanked Bafta for "including me among these beautiful performances".
The Still Alice star plays a woman struck down by Alzheimer's in the film and thanked her Scottish relatives who "poured love into me".
Eddie Redmayne has won the Leading Actor Bafta for his performance as Professor Stephen Hawking in The Theory Of Everything.
Accepting his best actor award, Redmayne recalled the "incredibly unfortunate" night he had to flee a previous Bafta ceremony to be sick with food poisoning.
He said: "It was one of the worst nights of my life. This is one of the best."
He thanked his own family, his "professional family" on the film and the Hawkings "for their trust in us, their generosity and their kindness".
Richard Linklater has won the Bafta for best director for his film Boyhood.
Actor Ethan Hawke collected the award on behalf of his friend and said Linklater would be "frankly p*****-off" to have missed the awards.
He thanked the child stars at the heart of the film and said: "There is no one in this room who loves cinema more than Richard Linklater."
The EE Rising Star award, the only Bafta voted for by the public, has been awarded to Jack O'Connell, the star of '71 and Unbroken.
Former Bafta president and filmmaker Lord Attenborough, who died last year, was remembered with tributes from the Duke of Cambridge and actor Robert Downey Jr at the ceremony tonight.
The Duke described him as "inclusive" and "a leader with a vision" and praised his "passion for nurturing, supporting and developing talent".
He said: "I hope that everyone who watches his films and learns about him as a person will be encouraged to follow his example."
Downey Jr, who played the title role in Attenborough's film Chaplin, said: "I'm sad. I miss you Dickie."
Patricia Arquette has been named Best Supporting Actress for her performance in Boyhood.
On collecting the award, she said: "I have been in a work of art here because of you, Richard Linklater."
J.K. Simmons has been awarded the Best Supporting Actor for his role in Whiplash.
Picking up the award from Reese Witherspoon, he said: "This whole experience has been a gift to me."
The Lego Movie has won the Bafta for best animated film beating off competition from Big Hero 6 and The Boxtrolls.
The Theory of Everything, about the life of Professor Stephen Hawking, has won the award for Outstanding British Film.
The award was presented by former England football star David Beckham with Professor Hawking and Eddie Redmayne both in the audience at London's Royal Opera House.
The film, starring Redmayne as the pioneering scientist, is widely expected do well at the Oscars later this month.