Theresa May is facing a chorus of Tory demands for a radical overhaul of state funding for public services as cabinet ministers and senior Conservative MPs back higher pay for millions of NHS workers, more cash for schools and a “national debate” on student debt.

The prime minister’s waning authority was highlighted as her health secretary, Jeremy Hunt, and education secretary Justine Greening lobbied for an easing of austerity and senior Conservative MPs insisted public services would be in growing peril without an urgent loosening of the purse strings.

Separately, Damian Green, the de facto deputy prime minister and a May loyalist, hinted at a wider rethink when he said there might need to be a national debate about the level of student fees, in order to appeal to younger voters.

The level of internal pressure for the abandonment of austerity puts chancellor Philip Hammond under huge pressure to consider raising taxes to fund any extra public spending. It comes as the official body that regulates nurses and midwives – the Nursing and Midwifery Council – prepares to reveal new evidence on Monday of a growing crisis in the recruitment of nurses.

Government sources made it clear that Hunt was prepared to take on Hammond and call for the lifting of the maximum 1% pay cap for nurses and other NHS workers, citing as evidence a hard-hitting report by the government’s own NHS pay review body published in March this year.

In the report, the government’s advisers on pay warned that the cap “will not be sustainable for much longer” and said the costs of plugging gaps caused by staff shortages could soon be greater than the savings. It also highlighted the effects of Brexit, saying “changes in the UK’s relationship with the EU may reduce the ability to fill shortfalls in staff numbers from overseas”.

There are also growing worries about a lack of nurses and other NHS staff in areas of the country where the cost of living is highest, notably London.

The Tory MP Dr Sarah Wollaston, a former GP who is seeking to extend her term as chair of the Commons health select committee, said: “We have got to address this and work out at the same time how to pay for a better settlement for public sector workers.” Another Tory MP, Dr Dan Poulter, who works as an NHS psychiatrist, said that while difficult choices had been made to improve public finances, “the time has come to lift the pay cap and reward nurses, midwives, doctors and other health care professionals”.

Jeremy Hunt is reportedly prepared to take on Hammond and call for the lifting of the pay cap for NHS workers. Photograph: Mark Thomas/Rex

A poll for the Observer by Opinium shows the extraordinary extent to which May has lost the trust of voters since the height of her popularity in April, and equally strikingly, since the June general election.

Over the same period, Labour leader Jeremy Corbyn, who has called for an end to austerity and the public sector pay cap, has soared in public esteem. On 19 April, May’s net approval was +21% (when the number who disapprove is subtracted from those who approve) while Corbyn’s was -35%. Now May is on -20% and Corbyn on +4%. Since the general election 61% of voters say their opinion of May has become more negative. Labour (45%) is now six points ahead of the Tories, who are on 39%, enough to give Labour a clear win if another election is called.

Last week Tory MPs were ordered to vote down a Labour amendment to the Queen’s speech calling for an end to the public sector pay cap. Hunt accused Labour of using the NHS as a “political football” in the vote.

But while the Conservatives do not want to be seen to be responding to Labour pressure, behind the scenes there is a growing view that May and Hammond will have to give a clear signal that the government will change direction before parliament breaks for the summer on 20 July. MPs and ministers then expect a change of policy to be confirmed in Hammond’s autumn budget. Many Tories say the £1bn deal to secure the support of the DUP has made the case for the public sector pay cap impossible to defend.

Greening is understood to have been pushing for months for more money for the schools budget, and is now said to be sympathetic to calls for teachers to be given a pay rise above the 1% cap, which is due to apply until 2020. Graham Brady, the chairman of the Tory backbench 1922 committee, said action on schools was needed.

“Those of us representing the worst-funded schools in the country have been very clear that a solution needs to be found that will relieve the pressure on those schools. I hope it will be possible to give some greater clarity before schools break up for the summer holidays,” he said.

Zac Goldsmith, the Tory MP for Richmond Park and former London mayoral candidate, said much progress had been made in education. “But the financial pressures are mounting fast and the government cannot avoid providing a better funding deal,” he said.

Green, the first secrtary of state, said yesterday that the level of tuition fees may need to be reconsidered in order to reach out to younger metropolitan voters. While £9,000-a-year fees allowed high quality courses and teaching, student debt had become a “huge issue”.

Answering questions after a speech at the Bright Blue think tank, Green said the only way to cut fees and retain standards would be to put up taxes. “Governments have to take money from everyone at work and companies that provide jobs to provide those essential services. And it may well be that this is a national debate that we need to have.”