Boris Johnson has waded into the escalating cabinet row over public-sector pay, throwing his weight behind calls for the 1% ceiling on wage rises to be lifted for austerity-weary workers including nurses and teachers.

The chancellor, Philip Hammond, has come under increasing pressure to ease spending constraints in several areas since the general election deprived Theresa May of her majority. Johnson is the latest cabinet heavyweight to demand a change of direction.

“The foreign secretary supports the idea of public-sector workers getting a better pay deal and believes the findings of the pay review bodies should be respected,” a senior government source told the Guardian.

His intervention follows a similar call from Michael Gove, the environment secretary – whose entry into the Conservative leadership race last summer thwarted Johnson’s own bid – and from the health secretary, Jeremy Hunt, and the education secretary, Justine Greening, who has demanded £1bn in extra schools funding.

It is fresh evidence that collective cabinet responsibility, which usually keeps major disagreements between senior ministers behind closed doors, has all but collapsed since the Conservatives’ majority was wiped out in last month’s general election.

Amid the calls for the pay cap to be lifted, the Treasury has been keen to stress that any extra spending would have to be made up from tax rises or spending cuts elsewhere.

Johnson believes the message on doorsteps was that pay and public services are pressing issues, a view shared by an increasingly vocal group of Tory backbenchers, including South Cambridgeshire’s MP, Heidi Allen, the former GP Sarah Wollaston and the MP for Plymouth Moor View, Johnny Mercer.

Downing Street appeared to hint at a change of heart over the controversial policy last Wednesday, acknowledging that the public were “weary” after seven years of cuts. But with the autumn budget still months away, the chancellor is refusing to have his hands tied and later the same day, May’s official spokesman repeatedly insisted that “the policy has not changed”.

The shadow health secretary, Jon Ashworth, said: “It’s clear that cabinet ministers are panicking but if they really wanted to show that they understood the concerns of public sector workers they would say now [that] they’re getting rid of the cap and allowing the pay-review bodies to come out with a fair pay settlement.”

The eight independent public sector pay review bodies offer recommendations to the government. But their findings are shaped by wider government policy, which since 2015 has been a 1% ceiling on increases in the wage bill, introduced by George Osborne and due to continue until 2019-20.

Gove told the BBC’s Andrew Marr Show: “They take account of that but they also take account of other questions. These pay review bodies have been set up to ensure that we can have authoritative advice on what is required in order to ensure that the public services on which we rely are effectively staffed and that people within them are effectively supported.”

The latest report from the NHS pay review body, published in March, warned of “significant supply shortages in a number of staff groups and geographical areas” and “widespread concerns about recruitment, retention and motivation that are shared by employers and staff”.

The most recent report on teachers’ pay, published last July, found that “recruitment and retention pressures have become more acute, creating a challenging climate for schools”.

The Institute for Fiscal Studies (IFS), a thinktank that analyses tax and spending policies, is also warning of increasing strain. “Recruitment and retention problems are emerging in the public sector following successive years of public pay restraint. The government’s current plan of 1% increases for the next two years risks exacerbating recruitment problems – and ultimately reducing the quality of public services,” said the IFS’s Jonathan Cribb.

Labour sought to capitalise on the government’s discomfort over public-sector pay by tabling an amendment to last week’s Queen’s speech calling for the cap to be scrapped.

Conservative MPs voted with the government but many subsequently expressed their disquiet. Mercer made a video message for his constituents, reassuring them that he hadn’t “had a lobotomy” and would put pressure on the government privately over the issue.

Johnson does not think easing the constraints on public-sector pay would have to mean ditching the government’s commitment to balancing the books. “He strongly believes the rises can be done in a responsible way and without causing fiscal pressures,” the source said.

Greg Hands, a former chief secretary to the Treasury and now a minister in Liam Fox’s international trade department, defended the pay cap on Sunday, saying it had helped protect jobs, and stressed the need for “budget discipline”.

“It’s very important to recognise what we have on public-sector pay. Actually by having that cap in place we have saved around 200,000 public-sector jobs,” he said on the BBC’s Sunday Politics. “There’s no change in government policy. We must live within our means. And that is the right thing to do.”

Cribb, of the IFS, said: “Higher public-sector pay rises would require significant extra resources for government departments to pay for the higher wage costs, unless departments make cuts elsewhere.”

In the run-up to the general election, the IFS said Labour’s policy of scrapping the cap would cost government departments and local government £6.3bn per year compared to the government’s plans – increasing to £9.2bn per year by 2021–22.

Johnson’s majority in his Uxbridge and South Ruislip constituency was cut in half – to just over 5,000 – at the general election and he is the target of an “unseat Boris” campaign by Labour activists, as the party seeks to capitalise on Conservative disarray and gear up for an early general election.

He denied laying the groundwork for a potential leadership bid in the immediate aftermath of the general election, describing reports that he hoped to topple the prime minister as “tripe”.

But with centrist Tories casting around for a champion and few Conservative MPs believing May can take them into another election – whenever it comes – Johnson is widely believed to harbour leadership ambitions.