Universal access to public services and improved educational opportunity hinge on the reversal of a $2.2bn cut to universities, the chair of Universities Australia will say in a speech on Wednesday.

Margaret Gardner, the vice chancellor of Monash University, will call on policymakers to reverse the Coalition’s two-year freeze on the demand-driven system at the National Press Club and release research on the value of collaboration with business.

Universities Australia aims to increase pressure on the Turnbull government and Labor, which has opposed the cut, but so far declined to say whether it will reverse it.

In the mid-year economic update, the Coalition unveiled a package of $2.2bn in cuts, the centrepiece of which is an unlegislated freeze on the demand-driven system for university places which Universities Australia has said will mean 9,500 places are unfunded in 2018.

In the speech, extracts of which have been seen by Guardian Australia, Gardner says the “ethos of universal access to public services, such as health and education, is central to the continuing project of Australian social cohesion”.

Gardner says the Rudd government’s move to uncap university places in 2009 was a “bold advance” that was supported by both sides of politics.

Since then enrolments from the poorest fifth of Australian households are up 55%, regional and rural students up 48%, Indigenous enrolments up 89% and enrolments of students with a disability up 106%, she says.

Gardner says the $2.2bn freeze “is really a cap on opportunity for all Australians”.

“And it isn’t just that this year, and in the years to come, there will be people who wished for and could benefit from a university education, who will miss out.”

Gardner urges policymakers not to “lock the door of opportunity on young Australians – nor on older Australians who need to retrain and reskill as their jobs change around them”.

On Friday the opposition education spokeswoman, Tanya Plibersek, said Labor had fought the $2.2bn cut to universities “every step of the way” but because they weren’t in legislation Labor was “powerless to stop them”.

“Of course we’re opposed to those cuts,” she said.

Labor has committed to restore $600m to tertiary and further education and spend a further $100m on upgrading facilities.

“So we are absolutely committed to proper funding for Tafe and universities but the question is not only about proper funding ... it’s about how will this system be fit for the future.”

Labor has announced it will review tertiary education and wants to make Tafe and university to be “equally attractive” to prospective students.

While the education minister Simon Birmingham has questioned why Labor is reviewing the demand-driven system if it supports uncapped places, Labor has insisted the review is not a precursor to cuts.

Universities Australia has commissioned modelling by Cadence Economics, to be released on Wednesday, which finds 16,000 companies that partner with universities derive $10.6bn in revenue from the collaborations.

Companies receive a return on investment of $4.50 for every dollar invested in research with a university, it finds.

Gardner calls for a 50% increase in collaboration. She has written to the Australian Industry Group, the Business Council of Australia, and the Australian Chamber of Commerce and Industry to spruik the “business case for collaboration”.

Birmingham is due to address University Australia’s conference in Canberra on Wednesday, in which he will discuss universities’ role in professional accreditation.

Birmingham will announce the government has accepted an expert panel’s recommendation that it should consider limiting professional accreditation bodies’ jurisdiction to matters that are profession-specific, to avoid overlap with accreditation assured by the Tertiary Education Quality and Standards Agency.