The Bridge which scooped several awards each.
The 89-year-old’s performance in Blithe Spirit at the Gielgud Theatre saw her follow in the footsteps of her mother, Moyna Macgill, who made her debut in the same stage almost a century ago.
Picking up her award for best supporting actress, she said: “I simply can’t believe it.”
The Murder She Wrote star, who was given a standing ovation, said: “I can’t remember a lot of things these days but I can remember my lines.”
She told the audience that theatre was “life and I’m glad that I’m still in it” and thanked them, saying: “Here I am creeping up to 90 and I feel a million dollars.”
Singer-songwriter Davies won the award for outstanding achievement in music for Sunny Afternoon which is based on his string of hits with the band and his life growing up in north London.
Accepting his award, he paid tribute to the people who had inspired songs including Waterloo Sunset, Dead End Street and See My Friends.
He said:”People are the source of my material, so the next time you’re sitting in a park and see someone like me looking at you don’t phone the police. I’m just writing about you.
“The world is a wonderful place to be in for people.”
Speaking backstage, Davies said he was already making plans for another musical but stayed tight-lipped about it saying only it would be an “original” and “spectacular”.
The show scooped three more awards with George Maguire, who plays Ray’s brother Dave in the show, named best supporting actor in a musical.
He thanked The Kinks guitarist, saying:”Thank you Dave for being you”, before the Olivier for best actor in a musical went to the man playing Ray - John Dagleish - who thanked the singer for “some of the best music ever written”.
It was also named best new musical and Davies dedicated the win to his three families - his cast, his real family in North London and The Kinks who he called “Four of the unlikeliest pop stars you’ve ever seen”.
The bash, which attracted some of the biggest names in Theatreland, also saw Mark Strong named best actor for his performance in A View From The Bridge, while Penelope Wilton won best actress.
Her performance as a mother whose lawyer son was imprisoned by the Nazis in Taken At Midnight saw her triumph over stars including Gillian Anderson and Kristin Scott Thomas.
Speaking to reporters backstage, Strong said he did not expect to win but his triumph made him want to keep working on the stage.
He said: “That is what theatre is about. If it’s good it allows us to examine ourselves, why we behave the way we do. “In an age of technology which is full of screens, whether they’re phones, computers or whatever we need a bit of that, we need a bit of the live experience.”
A View From A Bridge was also named best revival and its director Ivo Van Hove won best director.
The best actor in a supporting role award was presented by Sherlock duo Mark Gatiss and Amanda Abbington and went to Wolf Hall and Bring Up The Bodies actor Nathaniel Parker who plays King Henry VIII.
The musical Wicked won the This Morning Audience Award, before former Talking Heads frontman David Byrne performed one of the songs from his musical Here Lies Love.
Lorna Want, from the Carole King musical Beautiful, was named best supporting actress in a musical beating Nicole Scherzinger in the process.
Her co-star Katie Brayben, who plays King, was named best actress in a musical.
The night ended with Dame Judi Dench presenting Kevin Spacey with the special award in recognition of his work in London theatre, before the Hollywood star launched into a show-stopping performance of Bridge Over Troubled Water.
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