Students from the poorest 40% of families entering university in England for the first time this September will emerge with an average debt of around £57,000, according to a new analysis by a leading economic thinktank.

The Institute of Fiscal Studies said the abolition of the last maintenance grants in 2015 had disproportionately affected the poorest, while students from the richest 30% of households would run up lower average borrowings of £43,000.

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Jack Britton, one of the IFS report’s authors, said that changes in recent years have been “heavily focused on further reducing the cost to central government” and that it had made the system more unequal.

“Replacing maintenance grants with loans reduces the government deficit but results in students from low-income families graduating with the highest debt levels,” he added.

The economic thinktank’s conclusion immediately prompted a sharp political exchange between the main parties and elite universities over the fairness of student finance – and a hint from the minister responsible that amid soaring debts the system could be reviewed again.

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Gordon Marsden, Labour’s shadow higher education spokesman, said the IFS study made a nonsense of the government’s defence of the current system.

“From scrapping the maintenance grant to freezing the repayment threshold [at which students start repaying their loans], this government has focused on increasing the debt burden of students from disadvantaged backgrounds,” Marsden said.

“Under the Tories, student debt continues to rise with no end in sight, and students will now graduate with a shocking average of over £50,000 in debt. The government must decide if they believe a lifetime of debt and a tax on aspiration are the best way to fund our higher education system.”

Tuition fees were lifted to £9,000 a year in 2012 by the coalition, in defiance of promises made by the Liberal Democrats in the run up to the 2010 election.

During the 2017 election campaign, Labour promised to scrap tuition fees and hinted that it might also find ways of helping graduates with their existing borrowings. The pledges were credited in helping the party win over scores of young people and gain seats in university towns such as Canterbury.

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Writing in the Guardian, the higher education minister Jo Johnson describes as “misguided speculation” the idea government was likely to scrap the current system of loans that hiked from £3,600 a year in 2012.

But significantly, the minister went on to concede that the political climate makes demands for change hard to ignore, and pledged that he would also look again “at the details of the student finance regime to ensure it remains fair and effective”.

Johnson also attacked Labour and said that its policy was unaffordable. He said that Labour’s policy of scrapping tuition fees would cost a “mind-boggling” £100bn by 2025.

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Student loan debt has been soaring and its total value rose above £100bn for the first time earlier this year, underlining the rising costs young people face in order to get a university education. Outstanding debt on loans jumped by 16.6% to £100.5bn at the end of March, up from £86.2bn a year earlier, according figures released by the Student Loans Company.

Many debts will not even be paid off within the 30-year time scale.

The IFS also found that more than 77% of those taking out student loans will have some or even all of the loans paid off by the government because graduates will not earn enough to repay their loans within that time.

Defending the situation, Johnson wrote: “The fact some loans never get fully repaid is a deliberate subsidy for the lowest-earning graduates, not a symptom of a broken student finance system.”

Students from low- and middle-income families are also made worse off by the government’s decision to hold down the income level at which graduates must start repaying their loans to £21,000.

By leaving the figure unchanged the proportion of graduates who have to start paying back loans quicker increases because average wages are rising. The thinktank added that it means that students will have to pay back £4,000 more over their working lives than otherwise.

The government’s position was criticised by the elite Russell Group of research-led universities, which includes Cambridge, University College London and Manchester.

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“Higher education should also be affordable for students and it may be helpful for the government to consider how to address concerns over things like the interest rate applied to undergraduate loans,” said Sarah Stevens, the Russell Group’s head of policy.

The report also found that university income from teaching has boomed since 2012, with fees from teaching up by 25% per student. Arts subjects have particularly benefited, with universities receiving a 47% increase in fees income from those subjects. By contrast science or medicine courses received much lower increases in funding since 2012 because they are more expensive to run.

“Universities are undoubtedly better off under the current system than they were before the 2012 reforms,” said Laura van der Erve, an author of the report. “However, their incentives have shifted towards providing low-cost subjects. This does not sit comfortably with the government’s intention to promote typically high-cost Stem (science, technology, engineering and mathematics) subjects.”

The IFS also highlighted changes to the interest rates charged introduced since 2012, with students now charged 3% plus the retail price index on loans accrued while they are still undergraduates. From September, students will be forced to pay higher interest rates on their loans of 6.1% after a surge in inflation.

“Due to their higher principal debt, students from poorer households accrue the most interest during study; students from the poorest 40% of families now accrue around £6,500 in interest during study,” its briefing note states.

In contrast students accrued just £1,500 in interest under the system in force before 2012, the IFS said.