Private providers would take full advantage of reforms allowing all their students to access government loans in a shift that would help bring an "abrupt end" to the "cosy settlement" enjoyed by state-funded universities.
The prediction is made in an analysis by the Policy Exchange think tank, which says there is a "widespread intention" among private institutions to accept more regulation in return for access to student-fee support.
Student finance is already set for an overhaul after the government this week accepted many of the proposals from Lord Browne of Madingley's review of higher education - although tuition fees will be limited to an upper cap of £9,000.
The Policy Exchange report - Higher Education in the Age of Austerity - says Lord Browne's proposals to allow undergraduates on all courses, regardless of their institutions' status, access to public loans are "welcome and long overdue".
Noting that some private providers already compete on price with established universities, it predicts that this will drive efficiency in a sector where "weaker institutions are sheltered from genuine competition".
"The proposed reforms, if implemented successfully, will bring an abrupt end to this cosy settlement," it adds.
Lord Browne acknowledged the importance of private institutions in a speech at BPP last week, when he stressed that "if prices rise too high, there is room for new providers to enter the market and deliver higher education more efficiently".
Private sector pressure may end up one of the only drivers of lower fees, as some analysts have warned that Lord Browne's proposals could be undermined by a hard fee cap and a bid by many universities to charge between £7,000 and £8,000 to replace teaching-grant cuts.
According to a source, Lord Browne believes that a hard fee cap will only necessitate another review of the sector to reconsider the issue in a few years.
The government is proposing setting a "double cap" of £6,000 and £9,000, with those charging above the lower limit required to make pledges on helping poorer students.
David Willetts, the universities and science minister, told Times Higher Education that access conditions would be "stringent" and there would be "fallback powers" for institutions that did not "make progress" on widening participation, although he stressed that these would not involve controlling admissions.
Also accepted in principle are Lord Browne's proposals on student loans with a repayment threshold of £21,000, although high-earning graduates will accrue interest at a rate 3 per cent above inflation. There will also be more generous grants of £3,250 for students from the poorest families.
Scares and scrutiny
The likely impact of the government's Comprehensive Spending Review on the academy was spelled out last week in a survey of vice-chancellors by Gareth Thomas, the shadow universities minister.
The poll shows that some expect their teaching grants to be cut by between 75 per cent and 95 per cent.
John Denham, the shadow business secretary, said the government had denied "independent scrutiny" of the Browne Review by holding on to the raw data it had used.
Meanwhile, it has become clear that almost all of the £2.9 billion cut to higher education outlined in the CSR will be achieved by slashing the teaching budget - at least by 60 per cent, and probably by more than 70 per cent if widening-participation funds are maintained.
The smaller pot for teaching - which is to be targeted at "priority" subjects - could also be accessed by private providers under Lord Browne's proposals.
The Policy Exchange report calls for parity in other areas too, including a recommendation that all institutions face renewal of their degree-awarding powers every 10 years. As it stands, private institutions' powers are reviewed every six years, whereas publicly funded institutions keep theirs indefinitely.
It proposes that the minimum requirement on student numbers for degree-awarding powers be lowered from 4,000 to between 1,500 and 2,500, and calls for fewer restrictions on the use of the university title.
Considering the prospect of failing universities being taken over by private companies, the document says this would "probably involve" major players such as BPP or Kaplan.
However, it adds that the government must assure private firms that degree-awarding powers and university titles will not be jeopardised by such takeovers.