Rishi Sunak has signalled the end of a moratorium on new onshore wind projects in an attempt to head off a row with Tory MPs, his second U-turn in two days.

The prime minister and the business secretary, Grant Shapps, reached a deal on Tuesday afternoon that will pave the way for communities to be able to authorise such energy developments without unanimous support.

It came after the former levelling up secretary Simon Clarke tabled an amendment to the levelling up bill that would have ended a ban on new onshore windfarms. It was endorsed by Boris Johnson and Liz Truss, as well as the former chief whip Wendy Morton.

The government will now set up a consultation on scrapping the moratorium on new windfarms later this month, to run until March 2023, with the National Planning Policy Framework updated to reflect the outcome by the end of April 2023.

Government sources admitted the compromise was designed as a “fudge”, and insisted the bar for new wind projects would still be very high.

On Monday, Sunak was forced to drop compulsory housebuilding targets to see off another embarrassing rebellion, sparking concern that he was too weak to take on unruly backbenchers.

The target of building 300,000 homes a year in England will now be “advisory” and councils will be allowed to build fewer homes if they can show hitting it would significantly change the character of an area.

Senior Tories were keen for an agreement on windfarms to be struck before Keir Starmer’s clash with Sunak at prime minister’s questions on Wednesday, to try to neutralise an expected line of attack from Labour about dithering on the issue during an energy crisis.

Given the agreements with backbenchers, MPs are hopeful that the levelling up and regeneration bill that has been in limbo for weeks can be brought back for the second day of its report stage as early as next Monday.

Over the summer, Sunak had pledged during his ill-fated Tory leadership campaign to scrap plans to relax the ban on onshore windfarms in England.

Shapps has recently spoken out against the building of wind turbines, and was criticised for claiming some were now “so big” they could not be constructed on land. He did add that onshore wind was part of the UK’s “critical mix” of energy.

The topic has proved divisive among other cabinet ministers in the past, too. The chancellor, Jeremy Hunt, spoke out previously about his support for onshore wind. But Chris Heaton-Harris, the Northern Ireland secretary, said in 2012 he was “vehemently opposed to onshore” wind and led the rebellion of more than 100 Tory MPs against David Cameron that put pressure on the government to eventually outlaw new ones.

The climbdown by Sunak on Tuesday came after weeks of rowing between senior backbenchers, with Alok Sharma, the Cop26 president, also lobbying ministers to end the moratorium.

Sources said there were enough conditions and consultations attached to Sunak’s climbdown that opponents would not be too riled. The Tory MP John Hayes had been leading a counteroffensive against moves to relax the new wind projects ban, having previously warned it would be “immensely unpopular”.

Labour believes that Clarke’s proposals were still too restrictive – more so than for any other infrastructure, including incinerators and landfill sites.

Lisa Nandy, the shadow levelling-up secretary, said Sunak was “in office but not in power” and that the prime minister and Michael Gove were “being forced into this position because they’re too weak to stand up to another backbench rebellion”.

She added: “We will need to see the detail, but if it is a fudge that leaves in place a very restrictive system for onshore wind – the cheapest, cleanest form of power – it would continue to deny Britain lower energy bills and improved energy security during an energy crisis.”

Despite some Tory MPs – such as Hayes – arguing in an open letter that farm land would be sacrificed for windfarms, putting Britain’s food security at risk, the president of the National Farmers’ Union said putting turbines on farmland could make it more profitable.

“Our focus is we should be having much more individual wind turbines within a business so we can create far greater levels of self-sufficiency within a local area,” Minette Batters told the Guardian.

Rresearch from the Energy and Climate Intelligence Unit published this week found that the number of windfarms it said would be required to provide electricity for all 29m homes in the UK would take up less than 20% of land currently occupied by landfill sites.