The leaders of England’s biggest cities have demanded urgent government funding to install sprinklers in hundreds of tower blocks, warning that 21 months after the Grenfell Tower fire, residents do not feel safe.

Representatives of 15 city councils and local authorities from Newcastle to Bristol delivered a letter to Downing Street on Tuesday, backed by Labour, which has accused the government of failing to meet its pledge after the disaster to do “whatever it takes” to keep people safe.

The bill for the works could be as high as £1bn, according to some estimates, and would dwarf the £400m the government has already released to replace combustible cladding on social housing blocks over 18 metres in height.

The call for sprinklers to be installed in social housing blocks has also been made by the London fire brigade commissioner, Dany Cotton, who said: “Sprinklers save lives, they are not a luxury.” The Royal Institute of British Architects, the Association of British Insurers and the National Fire Chiefs Council have also made the demand.

Sarah Jones, the shadow housing minister, said the call was prompted by the government’s refusal to every single council request so far for cash to install sprinklers. The demand does not cover privately owned blocks.

Jones cited evidence that apart from explosions there had never been multiple fatalities in a building fully equipped with sprinklers in the UK and that since 2007 building regulations had made it a legal requirement that every new residential tower over 30 metres tall should have sprinklers.

She said: “In London, Labour research revealed that just 4% of tall council blocks currently have sprinklers. The government must step up.”

The government has said it s consulting on changes to the building regulations about fire safety and is considering submissions, including about sprinklers.

Croydon council in south London has said it will install sprinklers in its 25 tallest blocks and Birmingham city council has announced a £31m three-year programme to fit them in 213 blocks.

Jack Dromey, the MP for Birmingham Erdington, said “chaos and confusion” in government meant important domestic issues were being missed.

He added: “Lives are being put at risk by a government which won’t take vital action on the retrofitting of sprinklers.”.

The signatories to the letter to the housing secretary, James Brokenshire, include councils in London, Birmingham, Liverpool, Leeds, Nottingham, Newcastle, Sheffield and Manchester, alongside Solihull, Coventry, Dudley, Sandwell and Wolverhampton in the West Midlands.

They said funding would be “vital to safeguard and reassure many thousands of tenants across the country. Where councils have started sprinkler retrofitting programmes, we also request that those councils should be able to apply for funding retrospectively.”

The Ministry of Housing, Communities and Local Government has been contacted for comment.