LONDON — “The Inheritance,” a two-part, six-and-a-half-hour play about the legacy of AIDS in New York, dominated the Olivier Awards on Sunday night, winning four trophies at the British equivalent of the Tony Awards.

At the Royal Albert Hall in London, the play, by Matthew Lopez, won best new play, best director for Stephen Daldry, best actor for Kyle Soller, and best lighting design for Jon Clark.

It beat strong competition, including “The Lehman Trilogy,” the acclaimed family saga about the founders of the financial firm, which is playing at the Park Avenue Armory until April 20, and “Sweat,” Lynn Nottage’s Pulitzer Prize-winning play set in working-class Pennsylvania.

Mr. Lopez said in an interview that he hoped “The Inheritance” would transfer to Broadway, especially given the play’s setting. “We’ve seen a lot of Brits come over and take home Tonys, so I think it’s only fair really,” Mr. Lopez said, when asked about the play’s success.