LONDON (AP) ― Mischievous musical “Matilda’’ dominated British theater’s Olivier Awards on Sunday, winning seven prizes including a joint best-actress trophy for the four children who play the title role.

Written by the playwright Dennis Kelly, with music and lyrics by Australian comedian Tim Minchin, “Matilda’’ took more prizes than any show in the Oliviers’ 36-year history. Its trophies included best new musical and best actor for a cross-dressing Bertie Carvel as well as the prize for young performers Cleo Demetriou, Kerry Ingram, Sophia Kiely and Eleanor Worthington-Cox. The quartet, who each perform two shows a week, are all 12 or under.

Worthington-Cox, at 10, is the youngest person to win an Olivier.

“That’s pretty cool,’’ she said. “Scary. But I find that pretty amazing.’’

Matthew Warchus, who took the best-director trophy for “Matilda,’’ said he was often asked which of the lead actresses was his favorite.

“It’s a ridiculous question,’’ he said. “There’s four little miracles there.’’

The musical is based on Roald Dahl’s tale of an extraordinary little girl from an ordinary family. It has become a big hit for the Royal Shakespeare Company, which has transferred it to the West End and plans to open it in New York early next year.

Minchin praised the RSC for hiring two writers from outside the mainstream to create a family musical. “I think that’s a victory for risk,’’ he said.

The Olivier awards honor achievements in London plays, musicals, dance and opera. Winners in most categories are chosen by a panel of stage professionals and theatergoers.

The prize for best actor in a play went jointly to Benedict Cumberbatch and Jonny Lee Miller, who alternated the roles of a scientist and his monstrous creation in Danny Boyle’s National Theatre production of “Frankenstein.’’

Miller paid tribute to his director, saying the hit show had succeeded because of “Danny’s quest for honesty and truth.’’

Ruth Wilson was named best actress for playing a weathered woman of the world in “Anna Christie’’ at the Donmar Warehouse. The production of Eugene O’Neill’s maritime melodrama, which co-started Jude Law, was named best revival.

Wilson, who is currently filming action movie “The Lone Ranger’’ with Johnny Depp, thanked “Anna Christie’’ director Rob Ashford, because “you always cast a harem of gorgeous men for me to act with.’’

Sheridan Smith ― last year’s best actress in a musical for “Legally Blonde’’ ― was named best supporting performer in a play for her non-musical role in wartime drama “Flare Path.’’

Nigel Harman won the best supporting role in a musical prize for his recently ended stint as Lord Farquaad in “Shrek.’’

The best new play award went to John Hodge’s “Collaborators,’’ a funny and chilling look at authoritarianism based on the relationship between Soviet leader Josef Stalin and writer Mikhail Bulgakov.

The prizes were handed out during a ceremony at London’s Royal Opera House hosted by Imelda Staunton and Michael Ball, currently co-starring in “Sweeney Todd.’’

The show featured a live linkup to an Oliviers reception in New York, currently home to a glut of British theatrical talent. According to the Society of London Theatre, a quarter of the shows currently running on Broadway originated in London.

The audience award for most popular play, chosen by public vote, went to long-running favorite “Les Miserables.’’

There were special achievement awards for Tim Rice, lyricist of “Evita’’ and “The Lion King,’’ and Monica Mason, outgoing director of the Royal Ballet.