Councils could face a bill of at least £600m after the Government failed to commit to funding mounting fire safety measures in the wake of the Grenfell Tower fire.

A well-placed source suggested the figure could easily rise as further inspections are carried out.

Communities secretary Sajid Javid this week announced a new independent expert advisory panel would advise on ‘any immediate measures that can be put in place to make buildings safe' following the blaze, which killed at least 79 people in a London block of flats two weeks ago.

And prime minister Theresa May announced the appointment of Sir Martin Moore-Bick to head the public inquiry into the fire.

Cladding on 120 tower blocks across 37 local authority areas has been found to be ‘combustible,' prompting councils to urgently look at fire safety improvements, including the retrofitting of sprinklers.

So far, all samples of cladding tested have failed and Ms May has urged councils not to wait for the results before taking action.

In Camden, it was decided to evacuate four towers based on fire inspectors' concerns about a ‘combination of fire hazards'.

Local Government Association (LGA) chairman, Gary Porter, previously tweeted that Mr Javid had ‘OKd' the Department for Communities and Local Government (DCLG) to cover the costs of cladding and sprinklers following new fire inspections.

And Mr Javid seemed to confirm this in the House of Commons last week: ‘If there is a local authority that needs support, including funding support, we will work with them to provide funding support.'

However, when asked whether the DCLG would be providing funding, a spokesman declined to offer a firm commitment.

He said: ‘It is the landlord's responsibility to make sure people are safe.

'The department is working with councils on a case-by-case basis and a caseworker is appointed by the department to each council that identifies one or more building in its area that has failed the safety check.'

Labour leader Jeremy Corbyn has called for the Government to provide ‘emergency funds' for councils to check cladding and install sprinklers in tower blocks around the country.

He said: 'There have been two coroner's reports. Building regulations have not been overhauled and local authorities - while asked to act on them - have had their budgets cuts by 40%.

'When you cut local authority budgets by 40% we all pay a price in public safety.

'What the tragedy of Grenfell Tower has exposed is the disastrous effects of austerity, a disregard for working-class communities, and the terrible consequences of deregulation and cutting corners.

'I urge the prime minister to come up with the resources that are needed to test and remove cladding, retrofit sprinklers, and properly fund the fire service and police so that all our communities can truly feel safe in their own homes.

'This disaster must be a wake-up call.'

A LGA spokesman added: ‘We also continue to press the Government to ensure councils have the funding they need to support residents and carry out any new safety measures.'

Hammersmith & Fulham LBC already plans to retrofit sprinklers in the communal areas of all 66 of its high-rise blocks at a cost of £27m.

A spokesman added: ‘The money has to come from somewhere. We will have to make difficult decisions but this is of paramount concern.'

Nottingham City Council leader, Jane Urquhart, has written to prime minister Theresa May asking for the Government to fund any necessary work.

A council spokesman said: ‘Given the gravity of the situation that the Grenfell fire has revealed, we would expect the Government to provide financial support for such measures, as it has said it would.

'Reserves are finite and if there was no extra money promptly forthcoming from government other schemes like new housebuilding would be impacted.'

Birmingham City Council's leader, John Clancy, has written to the country's biggest local authorities asking them to come together to call for government funding.

Cllr Clancy said: ‘The cost of doing this for all local authorities with tower blocks is certain to be substantial and beyond the means of austerity-hit councils to afford in a timely fashion.

‘The Government should accept this is a national emergency that fully justifies establishing a fund to allow councils to fit sprinkler systems as a matter of urgency.'

Last week, Nicholas Holgate, chief executive of Kensington & Chelsea RLBC, which has faced widespread criticism of the way it handled the crisis, resigned, claiming he was forced out by Mr Javid.

Chairman of the Association of Local Authority Chief Executives (ALACE), Tracey Lee, said: ‘This raises worrying points of principle. We [ALACE] are critical of inappropriate interference in local government in relation to the employment of chief executives and senior officers.'

Council leader, Nicholas Paget-Brown, has apologised but remained in post after winning the backing of his colleagues in the days after the fire.

Lewisham LBC chief executive, Barry Quirk, is providing interim leadership support to the council.