More than 80 people were injured on Thursday night when part of a theatre in London's West End collapsed on to the audience during a performance.

Fire crews rescued people from the Apollo theatre on Shaftesbury Avenue, which was showing The Curious Incident of the Dog in the Night-Time. There were more than 700 people in the audience.

London ambulance service said there were 88 casualties, seven of whom were seriously injured, but none are thought to have life-threatening injuries. The Metropolitan police said they were not aware of any fatalities.

Some people were initially trapped inside the theatre, but all were rescued from the building soon after the collapse.

The wounded were taken into the foyer of the nearby Queen's theatre, which was turned into a makeshift treatment centre. Some were taken from there to hospital on board a red London bus, with a police escort.

Firefighters inspect the roof of the Apollo theatre following the collapse. Photograph: Sang Tan/AP

The collapse of part of the ceiling, which then brought down sections of a balcony, occurred at about 8pm. Part of the balcony started creaking before the collapse, and some audience members assumed that the noise was part of the show.

People were escorted out of the building covered in dust and debris, while others left crying, coughing and helping each other away.

Photographs from inside the theatre showed heavy beams and wood strewn across seats, which were coated in debris and dust. There were reports that after a storm earlier, water had begun dripping through cracks in the ceiling before it fell in, but this was not confirmed by authorities. A Westminster council surveyor was inspecting the building overnight to assess whether it was safe enough for a full inspection. The surveyor was expected to deliver a preliminary report on Friday morning.

London fire brigade's Nick Harding said: "We believe around 720 people were in the theatre at the time. A section of the theatre's ceiling collapsed on to the audience who were watching the show. The ceiling took parts of the balconies down with it.

"Specialist urban search and rescue crews were also called to the scene to make sure no one was trapped. Fortunately all those who were trapped have been rescued and treated for injuries or taken to hospital.

"A number of people were injured and ambulance crews are working hard to look after them. The latest information is that there were around 80 walking wounded, many of whom had head injuries. Around five have been taken to hospital with more serious injuries.

Khalil Anjarwalla said he, his heavily pregnant wife and her parents managed to escape from the theatre safely after "kilos of concrete plummeted from the ceiling".

"I was in the upper circle with my family when, about 45 minutes in, people started shouting and screaming. We thought it was part of the play, but the ceiling was crumbling.

Injured people receive treatment on a London bus. Photograph: Neil Hall/Reuters

"Within an instant the whole roof seemed to come down. We saw a lot of people completely covered in dust. I could hardly breathe. We had to get out, calmly."

Anjarwalla, a businessman from Kenya who was visiting his in-laws with his English wife, Aliya, said: "The actors just seemed to run from the stage. They had obviously seen what had happened. Thankfully, we are all OK. My wife is seven months pregnant but she is OK."

Andrew Howard-Smith, 68, said: "I saw the edge of the balcony come down. We were on the balcony below. In the production you had to hold on to the rail and lean over to see what was going on, and we were doing the same.

"Everybody must have got hold of the brass rail and just pushed it over, and then the edge came off. That was the only bit that came off, just the edge. It wasn't the whole of the balcony, just the front 2ft."

Libby Grundy, 65, said: "There was a bang, and then a huge cloud of dust. At first I thought it was a special effect. I heard somebody on the stage say, 'Oh, bloody hell', because they must have seen it.

"And then people realised it must be some sort of emergency and people started getting up. People didn't panic. People were quite shaky when they got out. There wasn't any screaming. People were scared, but they weren't screaming."

As news of the collapse filtered out, the author of The Curious Incident of the Dog in the Night-Time, Mark Haddon, tweeted: "It's been horrifying sitting here watching what has been happening at the Apollo this evening. I'm hugely relieved that no one has died and I hope that those who were seriously injured are okay. I'm sorry, too, that so many people went through such a terrifying experience."

Helen Whitten, from Hampshire, who was at the theatre in a family group of eight and was sitting in row B, said: "We heard this real creaking in the roof for about five or 10 minutes before it happened. People were looking up and wondering what was happening.

"One or two of us caught each other's eyes. You thought 'it does not feel right'. Someone in Row A decided 'this is the time to get out'. Once they started, they all got out. I think they trusted their instinct and thought 'this is not right, let's go' and at that moment it happened."

Another member of the group, Julia Clay from Oundle in Cambridgeshire, said: "It all happened right next to me. I was in seat 9 of Row A. The people who left were at about seat 14. They pushed past me very abruptly. I thought they didn't like the show for some reason and they were leaving because of that. Then behind me everyone got up. Then there was pandemonium.

"It was big, heavy chunks of plaster and lots of black dust. It's still in my throat. I still feel quite dazed."

A spokesman for the Metropolitan police said: "There is no suggestion at this stage that this was as a result of a criminal act, however, at this stage we of course are keeping an open mind.

The prime minister, David Cameron, tweeted: "I've been updated regularly on the Apollo incident. I'm grateful for the fast work of the emergency services in helping the injured."

A spokesman for London mayor Boris Johnson said: "He has spoken to the Met police commissioner and is liaising with the relevant agencies. His thoughts and prayers are with those involved in what is clearly a very serious incident."

The Apollo theatre is a Grade II listed building. Completed in February 1901, the theatre seats 755, and the balcony on the third tier is considered the steepest in London. It is not yet known whether it was that one which collapsed.

A spokesman for Nimax Theatres, which owns the Apollo, described the ceiling collapse as a "shocking and upsetting incident" adding that their "thoughts are with the audience and staff" caught up in the incident and that an investigation into the cause was under way.

Council leader Philippa Roe said: "We are obviously shocked to hear the news and our immediate concerns are with the people that have been injured. Our officers are on site and they will help emergency services wherever they can."