The communities secretary, James Brokenshire, has confirmed plans for a multi-million pound fund to fix private tower blocks wrapped in combustible Grenfell-style cladding in England after mounting public anger that dozens of freeholders and developers have refused to pay to make them safe.

About 20,000 people living in private leasehold homes are estimated to be affected by the risk caused by the now-banned plastic-filled panels, similar to those which helped spread the fire at Grenfell that killed 72 people.

Having spent months trying to persuade property companies to pay with only limited success, housing ministers have been persuaded of the need to step in with public funds, as the Guardian revealed on Wednesday.

Speaking on the BBC Radio 4’s Today programme, Brokenshire said: “We’ll be putting in place a new fund for private buildings to deal with this issue of safety and of leaseholders who live in these buildings. What we’re talking about here is the use of aluminium composite material cladding, the same cladding that was used on the Grenfell tower.”

“We’ve seen a number of building owners and developers coming forward and doing the right thing. But what’s been striking to me over recent recent weeks is just the time it is taking. And my concern over the leaseholders themselves, that anxiety that stress that strain, and seeing that we’re getting on and making these buildings safe.”

Some leaseholders have been forced to mount their own 24-hour patrols to make sure fires don’t break out, while others’ homes have become unsaleable. A survey of the impact on residents last month found some had turned to drink and drugs and others were suffering bouts of depression and suicidal feelings. The greatest number of affected buildings are in London and Greater Manchester and many belong to first-time buyers.

The standoff between leaseholders who say they cannot afford to pay bills of up to £80,000 each and freeholders and developers who say they are not obliged to pay under law has caused growing anger and frustration as next month’s second anniversary of the Grenfell disaster looms. Grenfell survivors have warned that a delay in tackling the problem means a second disaster is “in the post”.

A spokesperson for the Ministry of Housing, Communities and Local Government said on Wednesday that the lack of action by some private building owners was “completely unacceptable”.

“Due to lack of progress the government is looking at a range of new additional measures to get building owners to do the right thing,” they said.

Ministers have told campaigners that the decision lies with the Treasury. Those who have lobbied Hammond to release funds include Kevin Hollinrake, a Conservative member of the Commons housing select committee. He said on Wednesday: “We need to step in and provide a solution. That is going to include money and we are in conversation with the Treasury.”

Pressure has been growing on ministers to step in. The London mayor, Sadiq Khan, the housing charity Shelter and the Local Government Association (LGA), which represents town halls, have backed a national campaign fronted by leaseholders calling for public funds to strip off and replace the dangerous cladding on private apartment blocks over 18m in height.

Lord Porter, a Conservative peer and the LGA chairman, said: “Too many leaseholders are suffering stress on a daily basis because it is still not clear who will pay to fix their homes. This cannot and must not continue.”

Checks found 176 private residential towers were wrapped in the same aluminium composite material fitted to Grenfell Tower partly as a cosmetic improvement in a £10m refurbishment concluding in 2016.

But according to the government’s own figures, leaseholders in 93 private towers are not protected from remediation costs and works have been completed on just 10. The communities secretary, James Brokenshire, made £400m available to fix social housing blocks a year ago, moving money from an existing fund for affordable homes. As a result work on fixing council and housing association towers has progressed much faster.

However, there is concern any new money will only be made available to remove the aluminium composite cladding and not to fix other fire safety problems including high-pressure laminate panels which are also combustible and buildings where fire breaks supposed to stop fires spreading through cladding are missing or faulty.

Last week, the housing minister Kit Malthouse told parliament: “We have been engaged across government to consider additional interventions, so that progress can be made more swiftly.” He said he hoped to announce specific measures shortly.

He said leaseholders were currently protected from remediation costs in 83 out of 176 residential buildings. “The growing list of owners and developers who have stepped in includes Barratt Developments, Mace Group, Legal & General, Peabody, Aberdeen Asset Management and Frasers Property,” he said.

“In the social sector we are making good progress,” he added. “In the private sector, progress is slower; I absolutely admit that. We need to do something to speed that up, and we hope to increase the pace quite soon. Discussions are ongoing.”

• This article was amended on 10 May 2019 to make clear the funding plan is for England. Housing jurisdiction is devolved for Northern Ireland, Wales and Scotland.