Boris Johnson is facing potential defeat at the hands of Tory rebels over the cladding scandal with 38 MPs now supporting a backbench amendment to protect flat owners.

Stephen McPartland, who is leading on the amendment, revealed the figure and said campaigners were making “huge progress” towards ensuring leaseholders do not have to pay to fix historic fire safety defects identified after the Grenfell Tower disaster.

The prime minister suggested he agreed on Wednesday, insisting leaseholders “should not have to worry about the cost” of making good fire risks.

Housing minister Chris Pincher on Monday asked McPartland and his backers to withdraw their amendment because the government will ”very shortly” announce a financial solution.

But McPartland told HuffPost UK’s Commons People podcast he refused, and made clear that any proposal involving loans for leaseholders would be unacceptable as it would see many effectively losing money through building up debt on their properties.

The government has a majority of 80 so just two more MPs backing McParland’s amendment to the fire safety bill, due back in the Commons soon, could leave Johnson facing defeat.

Asked if the housing minister had offered enough, McPartland replied: “Absolutely not.

“The housing minister asked us to drop our amendment because they’re frightened.

“And we now have 38 Conservative colleagues signed up to the amendment, so we’re making huge progress and we’re going to continue doing that.”

McPartland accused housing secretary Robert Jenrick of “incompetence” over the scandal and suggested Pincher “doesn’t seem to have a grip of the issue”.

“It’s almost like he doesn’t actually fully understand it,” the Stevenage MP said.

Part of the problem is that the government in January 2020 changed advice on building safety, meaning buildings of all heights became embroiled in the crisis, rather than just those over six storeys, McPartland said.

This meant that instead of around 1,700 buildings, 100,000 buildings and more than four million flats became affected.

McPartland said campaigners estimate that between £20bn and £40bn is now required to fix the issue, as even second-storey flats with wooden balconies are subject to the advice.

He suggested the guidance could be changed to exclude houses on lower storeys and not include materials like wood, with more “risk-based assessment” of individual blocks.

The MP said: “I think one of the things that people are missing is that a lot of people are trapped in a position where they cannot sell these properties.

“When we hear about […] loans, I made it very clear in PMQs [prime minister’s questions] on Wednesday that I would not support loans to leaseholders.”

The issue reached a head this week after Labour called an opposition day debate on the scandal on Monday.

But McPartland said Labour should have been campaigning about it years ago, arguing Tory rebels are now the driving force behind policy that changes people’s lives.

“If you look at the cladding scandal it’s led by myself and my colleague Royston Smith in Southampton Itchen,” he said.

“The Labour Party should have been running that campaign for the last three years and they’ve not.

“If you look at a lot of the campaigns, the things that are changing the fabric of how people live, it’s actually Conservatives who are technically rebelling.

“But it’s a space and gap the Labour Party should have been in already.”

McPartland also revealed that some Tories expect Starmer to lose his position as Labour leader before the next election.

“I think from a Conservative Party view, we think he’s doing a good job as Labour leader,” he said.

“Internally we’ve always felt he’s only got another 18 months and then they’ll replace him, so we’re just basically waiting and seeing.”