Universities Australia has told the government to look elsewhere for budget savings, releasing an analysis that shows almost $4bn has been cut from the sector and its students since 2011.

The tertiary education sector is increasingly confident that the Turnbull government will finally drop its unlegislated plan to cut 20% of funding from universities but is seeking to head off a range of other possible cuts in the 9 May budget.

The university sector fears the government is planning to make up the lost savings with a possible 2-3% efficiency dividend on their base funding, and potential increases in the student contribution to degrees’ cost and a reduction in the Help student loan repayment threshold.

The Universities Australia paper found that cuts since 2011 under successive governments total $3.9bn including:

changes to the Student Start-up Scholarship ($1.41bn);

cuts to the Sustainable Research Excellence scheme ($648.8m);

removing performance funding for universities ($698.5m);

abolishing the Capital Development Pool ($298m); and

cuts to the Higher Education Participation and Partnerships Program ($90.7m).

The paper said that total commonwealth funding to universities had grown by 59% from 2009 to 2015 but added that was a consequence of “substantial enrolment growth”.

“However, in real (inflation-adjusted) terms, funding per university place grew by less than 1% each year between 2009 and 2015,” it said, warning that funding will not increase at all after a new indexation formula is introduced in 2018.

The Universities Australia chief executive, Belinda Robinson, said universities and their students “have already done more than their fair share of budget repair ... Enough is enough”.

“In this context, it is difficult to justify further cuts that would affect student affordability and put at risk the quality of education and research on which Australia’s prosperity depends.”

The Abbott government proposed a 20% per-student subsidy cut in the 2014 budget, along with full university fee deregulation. In the 2016 budget the 20% cut was delayed and deregulation was dumped.

An options paper developed an alternative proposal for universities to allow universities to introduce premium “flagship courses” to pay for the cut, which never passed the Senate and stands as a “zombie measure” on the budget books.

According to reports the government is set to abandon the plan for flagship courses and the 20% cut in the 9 May budget.

The Grattan Institute’s Andrew Norton has recommended lowering the income threshold at which students repay their Help debts from $55,000 to $42,000.

The education minister, Simon Birmingham, said the government would release a finalised university package in the budget.

Birmingham said that universities funding had “grown dramatically” in recent years, by 71% since 2009, due to the demand-driven system – twice the rate of growth of the economy at large.

The Turnbull government was “looking at what best encourages Australians to repay their Help debts”, he said.

The government aimed to encourage excellence in higher education, ensure students have support “while also making sure the system is sustainable for future generations so students yet to come have the sorts of opportunities this and other generations have had”.

“I guarantee that, whatever we do in the future, the Turnbull government will ensure Help student loans will continue to be one of the cheapest loans people will ever get,” said Birmingham.

Asked on Radio National whether universities could fund cuts out of operating surpluses, Robinson said surpluses varied between institutions and were not discretionary but rather “required” for ongoing research and building programs.

The Group of Eight universities chief executive, Vicki Thomson, echoed Universities Australia’s calls to exempt the sector from cuts because the sector had taken “significant hits” over many years.

“You have to wonder how sustainable the sector is if the government keeps making cuts at the edges,” she said, warning that universities may have to cut student equity payments, increase class sizes or cut capital infrastructure or research.

“Universities are good at keeping on keeping ... but something has to give.

“It’s true that universities are free at the point of entry, but we want to make sure students have the best opportunities while they’re there, and funding cuts put that at risk.”