Universities have said they need “significant financial support” from the Government as students change courses after being awarded higher grades.

Students were told on Monday they could receive grades based on teachers’ estimates following anger over the downgrading of thousands of A-level results.

Education Secretary Gavin Williamson remains under intense pressure despite apologising to pupils – and has repeatedly refused to say whether he will consider resigning.

In a letter to Mr Williamson from Universities UK, seen by the PA news agency, vice-chancellors warned of the financial difficulties some institutions face following the U-turn, and said they needed “significant financial support from Government to stabilise their finances”.

Sent on Monday, the organisation warned: “The move to using centre-assessed grades will rightly address the inequalities suffered by many students from disadvantaged backgrounds by use of the original algorithm.

“However, it will also result in significant overall grade inflation leading to significant decreases in planned enrolments at a number of institutions as students opt for higher tariff courses.

“Such institutions whose financial plans were based on the agreed temporary student number controls will now require additional government financial support.”

The University and College Union (UCU) and National Union of Students (NUS) have also signed a joint letter to Mr Williamson, warning the lifting of the student cap – which had aimed to prevent institutions from over-recruiting to make up for lost revenue as a result of Covid-19 – would “remove one of the only interventions that the government has made to help mitigate the financial impact of the Covid crisis on universities”.

The letter said: “While it is still unclear exactly what the distribution of domestic students across higher education will be, it is widely anticipated that institutions will move as much as possible to honour their offers.

“This will likely lead to expanded recruitment at high-tariff institutions at the expense of lower-tariff universities, shifting the financial pain from the Covid crisis onto many of the institutions that play a vital role in widening participation and social mobility.”

The letter added scrapping the cap did not “address the practical barriers that prevent many institutions from recruiting higher numbers than they originally intended in order to honour their conditional offers – including staffing and physical capacity”.

Leading universities have warned students who now have higher grades amid the policy change could still be asked to defer their place if there is no space left on their preferred course.

In some courses, such as medicine and dentistry, institutions may not be able to admit students this year.

The first meeting of a new taskforce set with tackling issues faced by universities following the Government’s exams U-turn took place on Tuesday.

In a statement, education minister Michelle Donelan said: “We are working closely with the higher education sector to understand the challenges facing universities and provide as much support as we can.

“I led the first meeting of our new taskforce and I will hold meetings every day with the sector to resolve these issues.

“We are supporting universities, including by announcing our intention to remove temporary student number controls and working with them to help them prioritise students and uphold their first choice either this coming year, or as a last resort the following year.

“We announced a package of support for the sector during the pandemic, including bringing forward tuition fee and research funding, and a scheme to assess any restructuring support higher education providers may need.”

However, Labour’s shadow education minister Emma Hardy criticised the decision not to invite the representatives of staff or students to the meeting.

In a tweet, she said: “How can a task force solve the crisis facing universities without also speaking to student and staff representatives?”

Meanwhile, the headteachers’ union has called for an urgent independent review of the exams grading fiasco.

Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), has written to the Education Secretary demanding a review to rebuild trust because “public confidence has been badly shaken”.

He said: “It seems to be clear that the statistical model for moderating centre-assessed grades was flawed and that it produced many anomalous results.

“But how did this happen, why were the problems not foreseen, and why were ministers not on top of this? Most importantly, what lessons can we learn for the future?”

It comes as GCSE students have been told they will receive their results on Thursday despite the Government’s U-turn on grading.

All schools and colleges will receive pupils’ GCSE grades from exam boards ahead of results day, the Joint Council for Qualifications (JCQ) said.

Exam boards said they have been “working hard” to provide centre assessment grades, based on teachers’ estimates, or moderated grades if they are higher.