During the cabinet meeting on Tuesday, the Prime Minister told ministers: “There will need to be a major national investigation into what’s gone wrong, when cladding that’s failing the tests has been fitted on buildings in this country over a number of decades.”

The probe could be a second phase of the public inquiry into the west London fire.

Today the Government revealed the total number of towers fitted with unsafe cladding had risen to 95 in 32 local authority areas in England. So far all of the samples submitted have failed fire safety tests.

The Government is now moving the scope of testing to schools, hospitals and other public buildings which may be judged to be at risk.

It also today established an expert advisory panel to look at any immediate action meeded so the public could be confident everything possible was being done to make all public and private buildings safe as quickly as possible.

The panel has a wealth of experience in fire and building safety, including testing processes. They will also draw in wider technical expertise as necessary to inform their advice to the Communities Secretary.

Dr Peter Bonfield said: “It is important that the best expertise from across our industry, the research communities, the professions and the public sector is drawn out to support the government and society at this critical time of need.

“I look forward to working with Sir Ken and drawing in expertise which will help address the challenges faced. I know that the will to positively contribute from professional bodies and others is strong and we will deploy this to support our work.”

It is intended that a first meeting of the Panel will take place this week.