Arterton joined co-host Stephen Mangan to introduce the show and the opening act, from the stage musical of Charlie and the Chocolate Factory.
The first award — for best revival — went to Ghosts at the Almeida Theatre and the Trafalgar Studios.
It was accepted by director Richard Eyre, who joked that the crowds outside the Royal Opera House had mistaken him for nightclub owner Peter Stringfellow, before paying tribute to the “most wonderful cast”, which includes Lesley Manville.
Ghosts triumphed again when another member of its cast, Jack Lowden, was named the best actor in a supporting role.
Eyre said the awards, which recognise commercial hits as well as subsidised theatres like the National, showed the healthy “ecology” of the theatre. He said: “For all the successes, you have to be able to fail and that is what subsidy gives you.”
Eyre beat big names including Mark Gatiss to the prize, before Sharon D Clarke won the best actress in a supporting role award.
The prize for best lighting design was shared between Charlie and the Chocolate Factory and Chimerica — Lucy Kirkwood’s play inspired by events in 1989 in Tiananmen Square, China.
The best sound design award was also shared, this time between Chimerica and the musical revival Merrily We Roll Along.
The award for best costume design, presented by Gok Wan and Alexandra Burke, went to Charlie and the Chocolate Factory, while Chimerica won best set design. The award for best entertainment and family show went to The Wind in the Willows, while Jeeves and Wooster in Perfect Nonsense was named best new comedy. Mangan gave up hosting duties for a moment to applaud the team behind the show, in which he played the idiotic but good-hearted toff Bertie Wooster.
The award for best new opera production went to Les Vepres Siciliennes, while the English Touring Opera won the award for outstanding achievement in opera.
Charlie and the Chocolate Factory star Nigel Planer and model Kate Moss presented a special award to impresario Michael White, whose West End credits include A Chorus Line and Annie.
Rory Kinnear beat Hollywood heavyweights Hiddleston and Jude Law to the best actor award for his performance as Iago in Othello at the National Theatre. Accepting his award, he said the part was one of the “most thrilling” of his life.
“All of us nominated in that category would agree it’s a lot easier to be recognised when you’ve got a decent part to play.”
Manville was named best actress ahead of stars including Judi Dench and Hayley Atwell.
Accepting her award — a bust of Laurence Olivier — she joked: “Oh Larry, where have you been all my life?”