The vice-chancellor of the University of Sydney fears that some children will be unable to afford a tertiary education due to the federal government’s reforms.

“I want the best students, not only those who can afford to pay,” Dr Michael Spence told Fairfax Media.

A Fairfax Media report has revealed that university leaders are concerned that deregulating course fees would force school leavers to select courses without knowing whether they will have to pay extra fees.

Prime Minister Tony Abbott says he can’t guarantee university fees won’t double because of his government’s deregulation of the sector.

But he can say they won’t have to pay a cent up front.

“There are lots of things that I can’t guarantee, because we live in an uncertain world, but I can guarantee that no one will have to pay a cent upfront because there’ll be these fee help loans to cover their up front costs,” he told the Nine Network on Thursday.

Mr Abbott said increased competition in the market would mean some fees go up.

“(But) I suspect others may well put their fees down,” he said.

Universities have called on the government to take more time to investigate any unintended consequences of the higher education changes before setting them in law.

“I don’t think social justice requires everyone to pay the same fee [in a deregulated system]. In fact it requires people to pay different amounts depending on their ability to pay,” Dr Spence said. “I think you have to be careful that you don’t create a trap where aspirational Australians, not just disadvantaged Australians, will be kept out.”

Concerns have been increased after a week of national protests culminating in yesterday’s march in the Sydney CBD, which saw thousands of angry protestors take to the streets chanting “F***k you Tony Abbott, f***k you”.

President of the National Union of Students Deanna Taylor said that the budget had been “cruel”.

“It was a cruel, harsh, mean budget and it’s going to absolutely savage higher education in Australia,” she told the crowd.

“In one swoop on Tuesday, the federal government not only attacked the universal healthcare system as we know it, schools, pensioners, hospitals, they also attacked higher education and young people,” Ms Taylor said.

NSW Greens Senator Lee Rhiannon has advocated, in some circumstances, for university campuses to be made no-go zones for conservative politicians.

It comes after Prime Minister Tony Abbott and Mr Pyne cancelled a visit to Victoria’s Deakin University on Wednesday on the advice of police.

Foreign Minister Julie Bishop, Mr Pyne and ex-Liberal MP Sophie Mirabella have all been targeted by protesting university students since the budget was handed down.

-with ABC