Vice-chancellors have threatened to withdraw their support for the higher education bill if the government does not formally restrict the powers of the planned Office for Fair Access.
Baroness Warwick, Labour peer and chief executive of Universities UK, was this week due to table an amendment to the higher education bill, ahead of its committee stage in the House of Lords, which would prevent Offa from interfering with universities' admissions policies and procedures.
A UUK spokeswoman told The Times Higher : "We expect to see the amendment taken up if we are to give our full support to the bill."
Under the plans for Offa, universities will have to sign access agreements before they could charge top-up fees from 2006. The agreements will commit institutions to ensuring fair access for underrepresented and non-traditional students. A university could be fined if it breached the terms of its agreement.
While the government has sought to reassure UUK that it has no plans to give Offa a remit over admissions policies and procedures, vice-chancellors want a commitment enshrined in the legislation.
"We will be pressing very hard for an amendment that explicitly excludes admissions from Offa's remit as at present there is nothing in the legislation that allows for this," the UUK spokeswoman said.
"We know there will be a lot of support for this amendment in the Lords, and it is a key issue for UUK. We want to see the amendment taken up if we are to give our full support for the bill. We want to see it enshrined in legislation."
Meanwhile, the status of part-time students emerged as a key battleground in the Lords.
Labour peer Lord Bartlett - supported by Labour colleague Baroness Boothroyd, chancellor of the Open University and former speaker of the House of Commons - has tabled an amendment to the bill that would ensure part-time students have access to the new grant and bursary packages available to full-time students under the plans to reform university funding.
The Liberal Democrats also confirmed this week that the unequal treatment of part-timers under the bill would form a key part of its Lords campaign.
A spokeswoman for the Department for Education and Skills defended the government's support for part-timers. "We want to encourage more part-time students to go to university, which is why we have more than doubled the amount available for support for such students over the next two years.
"That money will go towards the first-ever non-repayable grant for low-income part-time students, and some of that money will pay for all or some of the fees for more of this group of students than ever before.
"If all who are entitled to support actually applied for it, up to 97,000 students will benefit, whereas only 29,000 students received any kind of support under the current fee-waiver scheme administered by universities."
Lord Renfrew, a Conservative peer and Cambridge University professor, has tabled an amendment that would set up a national bursary system funded from the public purse to give all students a complete fee waiver if they come from families with incomes below about £15,000.
He has also called for the creation of a new academic salaries review board to address low pay among academics.