Theresa May has confirmed the government will allocate £200m to fix private tower blocks wrapped in combustible Grenfell-style cladding, after mounting public anger against dozens of freeholders and developers who have refused to pay to make them safe.

The Guardian first reported on Wednesday that ministers were poised to release the cash after lobbying from leaseholders who said the cladding was making them fear for their lives and causing serious mental health and financial problems.

The prime minister said the money would be made available to remove and replace unsafe aluminium composite (ACM) cladding from 170 privately owned high-rise buildings around England, although the funds would not be enough to fix all of them. Quotes for remediation have typically been in the £4m-£5m range and the £200m averages out at about £1.2m per building.

After the Grenfell Tower disaster claimed 72 lives, nationwide fire safety checks found 176 private residential towers were wrapped in similar aluminium composite material which the government said breached building regulations.

The housing secretary for England, James Brokenshire, made £400m available to fix the dangerous 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. Ten of the private towers have been fixed compared with 46 in the social housing sector.

Grenfell United, the survivors and bereaved group which has also been campaigning for money to be released for private tower blocks, met May at Downing Street last night before the announcement and welcomed the move as a “small step”.

A spokesperson for the group said: “Today’s announcement offers hope to people in dangerous blocks that the nightmare they have been living for nearly two years is almost over.

“This result is a testament to residents themselves, in social and private blocks, who refused to be ignored. The truth is we should never have had to fight for it. It is not a quick fix so we ask the government to also consider what financial support can be put in place while residents continue with night watches and wait for remediation works to start.”

The UK Cladding Action Group (UKCAG), a coalition of private leaseholders – who were facing bills of up to £80,000 each to fix their homes – which launched a campaign to secure funding in March said it was “good news”. It said the government had realised its preferred solution of asking building owners to do the right thing and pay for the works was failing.

But the group stressed the money would not cover the costs of removing all of the cladding, and would not cover the costs of other ongoing fire protection measures including 24-hour waking watch patrols of corridors, which leaseholders are paying thousands of pounds a month to maintain.

Rituparna Saha is one of the founders of UKCAG who lives in the Northpoint block in Bromley where leaseholders are facing a combined £3.5m cladding replacement bill. She said the announcement also introduced a “cladding lottery” because it only covered ACM panels of the type which helped spread the fire at Grenfell. Combustible non-ACM cladding and other fire safety problems such as faulty or missing fire breaks in wall systems would not be covered.

Sam Cole, a resident of City Gate, an affected block in Manchester, said: “Many Manchester residents with similar problems to us are also unlikely to benefit from this fund. And we will continue to fight with Manchester Cladiators [their campaign group] to support them.”

On Thursday May said: “We’ve seen a number of private building owners doing the right thing and taking responsibility, but unfortunately too many are continuing to pass on the costs of removal and replacement to leaseholders. Today I can confirm we will now be fully funding the replacement of cladding on high-rise private residential buildings so residents can feel confident they are secure in their homes.”

Brokenshire told BBC Radio 4’s Today programme he was concerned by “that anxiety, that stress, that strain” leaseholders, many of whom have found their homes to be worthless, were suffering.

Last month UKCAG released a survey which found some leaseholders had turned to drink and drugs and others were suffering bouts of depression and suicidal feelings.

Gary Porter, the chair of the Local Government Association, said: “This announcement will come as an enormous relief to leaseholders who are in no way to blame for the dangerous cladding on their homes. They have suffered for far too long. Reputable developers have done the right thing and paid for buildings to be fixed, but it would be wrong if the taxpayer had to pay the bills of those developers and contractors who are responsible for this crisis.”

• This article was amended on 10 May 2019 to make clear in text that the minister, and the £200m fund, cover England only. Housing jurisdiction is devolved, so Northern Ireland, Wales and Scotland are outside this funding decision.