Mr Spielberg picked up both the Best Director and Best Film awards during the ceremony, which was held at the Theatre Royal in Drury Lane. He also received the Lloyds Bank award for the year's most popular film, Jurassic Park.
The British actor Ralph Fiennes, who played the brutal Nazi commandant in the Spielberg film, took the Best Supporting Actor award.
The disappointments of the British at the Oscars were forgotten as Britain's academy recognised its own. Anthony Hopkins won Best Actor for The Remains of the Day, with Miriam Margolyes a surprise winner of the supporting actress category for her performance in The Age of Innocence.
Holly Hunter repeated her Hollywood success by taking Bafta's Best Actress award for her non-speaking role in Jane Campion's The Piano.
In the television awards, Helen Mirren took her third Bafta trophy by winning Best Actress for Prime Suspect 3. Robbie Coltrane, previously nominated for Tutti Frutti, this time won Best TV Actor for his role in Cracker. The controversial police drama, Between The Lines, won Best Drama series and Al Ashton's play about the homeless, Safe, was the Best Single Drama.
In the academy special awards section, Shadowlands won best British film and its director, Lord Attenborough, was later given a special award to mark his 25 years as a leading figure in Britain's film and television industry.
Lord Attenborough who, at the beginning of his speech, promised that he was going to cry, also announced to the academy that 'within weeks' he would be standing down as vice-president to make way for younger blood.
The Richard Dimbleby Award for contribution to factual television was won by Joan Bakewell, who was once memorably referred to by Frank Muir as the 'thinking man's crumpet'.
Ms Bakewell told the audience that the description was often hard to live down.
A special award was also given to the actress Thora Hird, with the academy's prestigious fellowship being awarded this year to the chief executive of Channel 4, Michael Grade.
Next year, the academy's annual writers' award will be known as the Dennis Potter Award in recognition of the terminally-ill writer's work in film and television.
THE LIST of Bafta award winners:
Fellowship Award: Michael Grade. Special Awards: Lord Attenborough and Thora Hird. Alexander Korda Award (outstanding British film of the year): Shadowlands, directed by Richard Attenborough. Richard Dimbleby Award (the year's most outstanding personal contribution in factual television): Joan Bakewell.
Best film: Schindler's List, directed by Steven Spielberg. David Lean Award (Best achievement in direction): Steven Spielberg, Schindler's List. Best leading actress: Holly Hunter in The Piano. Best leading actor: Anthony Hopkins in The Remains of the Day. Best supporting actress: Miriam Margolyes in The Age of Innocence. Best supporting performance: Ralph Fiennes:
Best single drama: Safe (Screenplay) David M Thomson, Antonia Bird and Al Ashton. Best drama series: Between The Lines (Peter Norris). Best Light Entertainment Programme or series: Rory Bremner . . .Who Else? (Geoff Atkinson and others). Best comedy programme or series: Drop The Dead Donkey (Andy Hamilton and others).
Best Actress: Helen Mirren, Prime Suspect 3. Best Actor: Robbie Coltrane in Cracker. Best Light Entertainment Performance: Richard Wilson - One Foot In The Grave; One Foot In The Algarve. Lloyds Bank People Vote for most popular film: Jurassic Park.