The towers in 15 council areas were identified as part of a national operation to identify at-risk buildings in the wake of the Grenfell Tower disaster.
The local authority areas with buildings that failed tests include Manchester, Portsmouth, Plymouth, Hounslow, Brent and Camden.
The Government has said it is not identifying other areas until residents have been notified, so as not to cause undue concern.
Test results are being sent to local landlords and fire services, with councils to decide on what course of action is needed and to inform residents.
Labour leader Jeremy Corbyn described the failed tests as a "nationwide threat" as he urged the Prime Minister to convene the Government's emergency committee to provide a "national response".
The Liberal Democrats demanded the Government declare a civil emergency, create a fund to compensate those evacuated from their homes and guarantee anyone told to leave their properties they won't have to pay council tax until they return.
Thousands have already been evacuated from high-rise blocks in Camden, north London, although other local authorities will make their own decisions based on the nature of their area's housing stock.
Brent Council leader Muhammed Butt told Sky News the high-rise block in his area that failed the Government's fire safety test has been checked by the fire service and evacuation was not deemed necessary.
Cladding has been removed on two Portsmouth tower blocks after being found to be a fire risk, although local officials insisted the buildings were still safe for residents to stay in.
The Prime Minister said it is possible for some councils to take "mitigating action" on tower blocks, but in other cases it had been necessary to move people out.
Speaking at an event celebrating Armed Forces Day in Liverpool, Theresa May revealed "it wasn't just a question of the cladding" but "a number of other issues" with the Camden tower blocks that concerned the fire service.
The Prime Minister said the Government would ensure councils take "immediate action" over the failed tests, adding: "Absolutely our first priority is people's safety."
Local authorities and the Government are together "making sure the resources are there to ensure what is needed to keep people safe is being done", including finding alternative accommodation for those told to leave their homes, Mrs May said.