About nine out of 10 NHS trusts say they have hospitals containing asbestos, the BBC has learned.
Of the 211 trusts to respond to a BBC inquiry, 198 said they ran hospitals containing the material, which was once widely used in construction but can cause illnesses including cancer.
An MP has called for an audit to find out the extent of the problem.
NHS Improvement said strict regulations meant asbestos in buildings was registered and safely contained.
The BBC sent Freedom of Information requests to all 243 NHS trusts in Britain.
Asbestos is a naturally occurring fibrous mineral and was widely used as a building material between the 1950s and 70s.
It is potentially dangerous when inhaled and may give rise to asbestos-related diseases such as mesothelioma, a cancer of the lining of the chest, which causes more than 5,000 deaths in the UK each year.
Jo Stevens MP, chair of the All Party Parliamentary Group for Occupational Health and Safety, urged the government to conduct an audit to "ensure every trust knows the extent of asbestos on their premises and has a plan for dealing with it".
She said: "If it's there it will at some point become dangerous if it's disturbed or if it deteriorates, so I'd like to see long term plans and long term strategies in place for its removal from all buildings.
"I appreciate that you have to prioritise what you do and so that's why there should be an audit of buildings so that the dangerous areas are dealt with first as a priority."
The BBC also found 352 claims were made against health trusts between January 2013 and December 2017 by people who had developed asbestos-related diseases in NHS buildings.
According to the trusts, those claims resulted in payouts of about £6.8m, though three legal firms told the BBC they had won compensation claims totalling more than £16.4m in the same period.
Mags Portman, 44, a sexual health and HIV consultant from Leeds, was diagnosed with mesothelioma in January 2017.
She believes she may have been exposed to asbestos 20 years ago when she was a junior doctor working at Law Hospital in south Lanarkshire.
When the hospital was demolished in 2009 about 1,300 tonnes of asbestos-related materials were removed.
She said: "There is a cruel irony thinking that asbestos is still present in hospitals when people go there to be made better and they may well be exposed to something which they're not aware of.
"Until this happened to me I didn't really know what asbestos was or where to find it but when you learn about it you realise it's everywhere."
Charity Mesothelioma UK has said it was so concerned about the presence of asbestos in hospitals it was launching a research project into the impact on hospital workers.
"I've lost count of the number of people who have developed mesothelioma as a result of being exposed to asbestos in our hospitals," Liz Darlison, founder of the charity, said.
"I'm not surprised, a lot of our hospitals were built in the second half of the last century when we were at the peak of importing asbestos into this country."
NHS Improvement said "many parts of the NHS estate date from an era when asbestos was widely used", adding that "asbestos is considered safe if it is undisturbed".
A spokesman said: "When building or other work is carried out, experts are brought in to safely dispose of it.
"We will continue to work with trusts to ensure their estates are a safe environment for patients and staff."