Ministers are to pave the way for an overhaul of university funding, with tuition-fee cuts, a cap on student numbers for certain courses and minimum qualifications among the options being considered in a soon-to-be-published consultation.

The long-awaited consultation document, intended as a response to the Augar review of tertiary funding, is to list potential policies designed to lower the cost to the government of financing England’s student loan system, after ministers and advisers failed to settle on a central option.

Divisions between No 10, the Department for Education and the Treasury over alternative policies means the consultation is to include what one sector leader called “a menu of unpalatable options” that have been argued over behind the scenes for several months.

The options include a return to student-number controls, abandoned in 2015, as well as setting minimum entry requirements such as barring school-leavers without GCSE passes in maths or English from accessing student loans.

The cut in undergraduate tuition fees recommended by the review conducted by Philip Augar in 2017 – from £9,250 down to £7,500 – is also among the options, including differential fees for certain courses such as nursing, sciences and maths, to encourage greater uptake.

Another option is freezing fees at their current level and letting inflation erode their value. When tuition fees were set at £9,000 in 2012 the intention was for increases to keep pace with inflation. But since being raised to £9,250 in 2016 ministers have refused to go further, meaning their real value has declined by 12%.

The Treasury in particular is keen to lower its exposure to student loans by directly cutting fees and increasing repayments, while No 10 and the DfE appear to favour more indirect means such as minimum entry requirements and course caps.

Gavin Williamson, the education secretary, has raised using school grades as a bar for entry, saying he found it “hard to understand” why students unable to get a GCSE pass should be able to study at degree level at the age of 18. “This is obviously something we’re going to be consulting on,” Williamson told a Higher Education Policy Institute (Hepi) conference last month.

A DfE spokesperson said: “As the education secretary set out in his recent speech at the Hepi conference, we are developing our plans to consult on further reforms to the higher education system and we will set this out in more detail in due course.

“We continue to consider the recommendations made by the Augar panel carefully alongside driving up quality of standards and educational excellence and ensuring a sustainable and flexible student finance system.”

The consultation comes as bumper numbers of school-leavers and older students apply for places on higher education courses, as revealed this week by the Ucas admissions service. About 44% of 18-year-olds in England have applied for places next autumn.

The government’s latest forecasts are for total loans to rise from £19bn this year to £22bn within five years’ time, thanks to the number of new students entering higher education.

The policies in the government’s consultation are aimed at reducing the rate of unpaid student loans. Under the current system, graduates begin repaying their loans when their annual earnings reach £26,000, while all outstanding loans are wiped 30 years after graduation.

The average graduate debt is expected to reach £47,000 for this year, with 54% of loans written off as the Treasury’s resource accounting and budgeting (Rab) charge. Only 12% of graduates are expected to repay their loans in full, while 33% are expected to not repay a penny after 30 years.

Nick Hillman, Hepi’s director and a key government adviser when the current loan system was drawn up, argues that lowering the repayment threshold makes more sense than the other options being offered.

Research published by Hepi found that lowering the repayment threshold to £19,300 would nearly halve the numbers who make no repayments, and double the proportion who repay their full loans to 24%. But the average graduate would pay £10,000 more than they do now.

“Higher education reform is never easy because voters do not vote for universities to take precedence over other public services. Without greater public funding, something has to give,” Hillman said.

“New number caps is by far the worst option, especially when the number of 18-year-olds is shooting up. Underfunding institutions also does not make sense. So you’re left with bringing the loan system back into equilibrium.

“Perhaps when 80% of people go to higher education, taxpayers will be more willing to foot the bill. Until then, we need to find the least bad option, which seems to be asking the beneficiaries to pay a higher proportion of the costs.”