Social landlords have warned they are facing a bill of more than £10bn to fix fire safety problems after the Grenfell Tower disaster and that much-needed affordable housebuilding is in jeopardy unless the government funds a bailout.

The cost is at least 25 times greater than the £400m budgeted for so far by ministers for housing associations to remove Grenfell-style cladding. It emerged as pressure grows on Downing Street to sanction a separate bailout of private leaseholders estimated at more than £2bn, with hundreds of thousands of homeowners unable to sell or mortgage their homes.

The National Housing Federation chief executive, Kate Henderson, revealed the scale of the cost to the Guardian as landlords discovered scores of their blocks were wrapped in other combustible materials and suffered from other safety flaws which under new government guidance must be fixed to ensure the safety of their 6 million residents. It is a conservative estimate and the NHF said the bill would “easily exceed” £10bn.

As well as reducing the number of homes that housing associations can build, the cost also means services to existing residents are likely to be hit.

The National Housing Federation and the Manchester Cladiators, a leaseholders campaign group, will this week write to the chancellor, Rishi Sunak, calling for urgent funds in the 11 March budget. Leaseholders will also meet the housing secretary, Robert Jenrick, to press their case for their own bailout.

The bill for fixing both social and private blocks now looks likely to reach the equivalent of the annual budgets for the Home Office and Foreign Office combined.

“Housing associations are doing everything they can to make their buildings safe as quickly as possible,” Henderson said. “However, following the latest advice from the government, the potential costs of this huge programme of work are spiralling.

“We are calling on the government to provide a building safety fund to cover the upfront costs of these essential works, so they can be carried out quickly and efficiently. Without this funding there is likely to be a detrimental impact on housing associations’ ability to build much-needed new affordable homes and provide services to their residents and their local community.”

Last month, one of the country’s largest social landlords, L&Q, said it was halting the purchase of new land and would defer work on projects beyond its existing commitments. It has earmarked £250m to spend on fire safety works on its existing estate.

The 15 largest London housing associations have estimated they face a £4.3bn bill which could result in them building tens of thousands fewer new houses.

The Grenfell public inquiry resumes on Monday, when the architects of the disastrous refurbishment which resulted in the loss of 72 lives will give evidence for the first time. Andrzej Kuszell, the founder of Studio E Architects, and Bruce Sounes, the project architect on the Grenfell refurbishment, will be cross-examined after the attorney general granted witnesses an assurance their oral evidence would not be used against them in future criminal prosecutions.

The government has repeatedly resisted calls to spend more on fixing fire safety problems. It committed to fund the removal of the specific type of aluminium composite material (ACM) panels used on Grenfell arguing these present the greatest safety risk.

But it will not fund the removal of other combustible materials even though fires have destroyed wood and high-pressure laminate facades in blazes in Barking and Bolton. On private buildings, where leaseholders are facing bills of up to £100,000 each, it has refused to fund works on anything but ACM, despite cross-party pressure in parliament and demands from the mayors of Greater Manchester and London, Andy Burnham and Sadiq Khan.

More than 500,000 leaseholders are estimated to be living in towers wrapped in combustible cladding that freeholders and developers are refusing to fix, arguing it is not their responsibility. Many are unable to sell their homes or remortgage them. There have been widespread mental health problems as a result of the stress caused with residents reporting depression, anxiety and even suicide attempts.

The Ministry of Housing, Communities and Local Government said: “The government has taken urgent action on building safety, including committing £600m for remediating high-rise buildings with unsafe ACM cladding in the social and private sectors.

“Residents’ safety remains our upmost priority. Cost should not be a barrier to remediation and there is no excuse for building owners not ensuring that residents are safe in their homes.”