Westminster Council, the local authority for the area, said the safety inspections turned up no immediate problems.
"Making sure people are safe when they come to the West End is an absolute priority," said council leader Philippa Roe.
London police said they had ruled out criminal activity as a cause for the partial ceiling collapse on Thursday night. One line of inquiry for investigators is whether a brief but intense rainstorm an hour before was a factor.
Witnesses described chaos and panic as large chunks of plaster, wooden beams and dust rained down on the Apollo's audience 45 minutes into a performance of "The Curious Incident of the Dog in the Night-Time."
"I thought, maybe this is part of the play," said Scott Daniels, an American tourist from the Dallas area. "All of a sudden, plaster starts raining down, huge hunks of plaster ... The lights went out and everything filled with dust - everybody was coughing and choking."
London Ambulance Service said Friday it had treated 79 people, 56 of whom were taken to local hospitals in ambulances and commandeered London buses. Of these, 47 were "walking wounded" with minor injuries, while nine people "had suffered more serious injuries including head and back injuries."
Nimax Theatres, which owns the Apollo, called the incident "shocking and upsetting."
Like many of London's West End theaters, the Apollo is more than a century old, built in 1901. It seats 775 people.
The Theatres Trust, which helps preserve Britain's historic playhouses, said theater plasterwork in London is inspected regularly and certified by independent experts.
Westminster Council said an investigation was under way and an initial assessment by surveyors had found that the Apollo's ceiling structure remained sound. It also said the Apollo's health and safety checks were all up to date.
The building remained cordoned off to the public Friday. The National Theatre, producers of "Curious Incident," said performances had been canceled through Jan. 4.
Marc Sinden, director of the documentary series "Great West End Theatres," said despite the accident, London's theaters are extremely safe.
"These theaters have been around for a very long time, but they are looked after and regularly maintained. They are looked after daily," he said.