Would-be doctors hoping to study medicine are struggling to secure places at oversubscribed medical schools after the climbdown on A-levels in England threw offers into disarray.

Universities say they have been bombarded with calls from angry families, some threatening legal action, if a place is not made available for their child.

Many students planning a career in medicine lost their places after results were downgraded by the government’s standardisation algorithm. Now, armed with the improved grades, some are too late to get into their school of choice as numbers are limited and expensive for institutions, and spaces have been filled.

Reluctant to turn away would-be doctors during the ongoing Covid pandemic, the Department for Education (DfE) came up with a series of proposals to try to remedy the situation – but most were rejected as impractical by universities.

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Meanwhile, several Russell Group universities reported having more than 1,000 students appealing for places they previously lost because of moderated grades that were later scrapped by the government and replaced by teachers’ recommended grades.

With new results yet to be confirmed by the universities’ admissions service Ucas, insiders said on Tuesday the sector was paralysed with uncertainty. Admissions workers fielded calls from distraught students throughout the day.

A Tory MP suggested students should be compensated with reduced tuition fees. Huw Merriman told the BBC: “This must have been one of the most unsettling and uncertain and upsetting things for [students] – A-level grades are a momentous and worrying time as it is – so I think to make it up for them we should be looking at what their student loan provision should be for the year coming into university.”

While lower-tariff universities waited to find out how many students they might lose to more selective institutions as candidates attempt to trade up, some members of the Russell Group were chasing private accommodation providers to see how many more students they might be able to absorb.

Universities UK, which lobbies on behalf of mainstream higher education, wrote to Williamson with a plea for more funding, claiming that some universities “will lose out from this very late policy change and will need significant financial support”.

UUK asked the government to “urgently put in place alternative forms of support” but its plea is likely to fall on deaf ears at the Treasury and the DfE, which is eager to use the crisis to reshape the sector.

The DfE announced the lifting of the student numbers cap on Monday amid the U-turn, and universities have been urged by the government to increase recruitment to ensure students with the required grades get places. But vice-chancellors warned of physical constraints, particularly with social distancing requirements.

Medical and dentistry students are particularly problematic as course numbers are limited and competition for places fierce. It costs upwards of £50,000 a year to train a medic, so taking on more students has significant financial implications and placements have to be found in the NHS.

Prof Richard Harvey, the academic director of admissions at the University of East Anglia, said it had 185 medical places but was grappling with a possible overshoot of up to 50 students. The situation is likely to be replicated at medical schools across the country.

“I have 1,500 emails in my inbox from angry people – mostly medics – all trying to work out what the hell they do now,” he said, calling on the government to release more funds for additional places.

“It’s perfectly possible for ministers to convert an apology into something that’s meaningful, but that means opening the cheque book and fixing the problem. Especially as we were all clapping carers not so long ago. Weren’t we all meant to be supporting the NHS?”

Some leading universities warned that students who now have higher grades as a result of the policy change could be asked to defer their place if there is no space left on their preferred course. Concern is growing, however, about the knock-on impact on pupils due to sit their A-levels next summer, who will face greater competition for places following this year’s overspill.

The University of Cambridge relaxed its admissions criteria following a call from 18,000 students and alumni. Applicants who were made an offer that was not confirmed following release of initial results will be admitted if their centre assessment grades now meet the conditions of their offer, although a deferral to 2021 will be required for some offer holders.

Nick Petford, the vice-chancellor of Northampton University, warned there would be “a lot of disappointed students” in coming days. “It’s really causing us – and students – a level of uncertainty that we don’t need at this time when we are planning for Covid. Twenty-four hours ago we had a really clear picture of what the number of students looked like. Now that’s all been thrown up into the air.”

Prof Mark Goodwin, the deputy vice-chancellor (global engagement) at the University of Exeter, said just over 400 students had indicated they would appeal. “I guess you can anticipate that the more selective institutions will have to take more students because of this, but it’s difficult to try to predict student behaviour, now that some of them have secured places with other universities through clearing.”

Sir David Bell, the University of Sunderland’s vice-chancellor, said it was too early to tell what the scale of the impact would be. “At the moment we are not seeing much movement,” he said, though he estimated about 100 newly recruited students could be entitled to return to their first choice of university with their new grades.

Jo Grady, the general secretary of the University and College Union, said: “Staff are now facing unbearable workloads dealing with the government’s exam results fiasco, after already facing cuts and threats of redundancies due to its incompetence during lockdown.

“Removing the student number cap means certain universities can hoover up students, hitting the finances of other institutions. It now needs to provide substantial financial support to the sector so that universities can protect all jobs, safely welcome students and continue to provide world-class teaching and research.”