Universities UK has signalled unhappiness with the government over "poor quality" student visa rules by advising institutions not to apply to become a "highly trusted sponsor" and by venting its criticisms in Parliament.
Higher education institutions have a deadline of 30 June to apply for the sponsor scheme, which is part of a tightening of student immigration rules ordered by the prime minister to crack down on abuse by economic migrants.
The UK Border Agency (UKBA) said highly trusted sponsor status would ease the bureaucratic burden on universities while preventing abuses of the immigration system.
But others fear that universities' international reputations and recruitment will be damaged if they fall short of exacting requirements and fail to qualify for the annually renewed status.
One critic described the scheme as a "sword of Damocles".
Sponsors must ensure that no more than 3 per cent of international students fail to complete their courses, and university staff will have to mount in-depth background checks on prospective students - detailed in a 21-page UKBA document.
UUK advised members not to apply for the highly trusted sponsor scheme in its current form, after it was introduced without any formal consultation of institutions.
The concerns emerge as income from international students grows ever more precious to universities in the wake of public funding cuts.
There was fierce criticism of the government over the student immigration changes in a House of Lords debate earlier this month, following lobbying by UUK.
Lord Avebury, Liberal Democrat Home Office spokesman, said the process by which the rules were changed was "fundamentally wrong and flawed".
UUK had referred to "poor quality and unclear documentation", he told the House.
The highly trusted sponsor scheme was initiated on 6 April, with universities gaining interim status. They have been given until 30 June to apply for full status.
Lord Avebury said that institutions "do not like the way that these changes transfer the responsibility for immigration control from the UKBA (to universities and colleges) ... and impose severe penalties on them if they fail to carry out enough of the 21 pages of tests or if more than a small proportion of those granted certificates of approval go absent or fail to complete the course".
He said he wanted the Labour government to guarantee that if it were re-elected, it would "never again try to push through material changes to the immigration rules affecting people and institutions without any of the safeguards that exist to ensure informed parliamentary scrutiny and to prevent flawed legislation".
Lord West, parliamentary under-secretary of state in the Home Office, replied that "given concerns about the security of immigration control, it was decided that it was not appropriate to conduct a formal written consultation".
Critics within higher education argue that the tightening of the Tier 4 student visa system - introduced in March 2009 - was a hasty, politically driven move.
Attention should have focused on making accreditation arrangements for private-sector colleges more robust, they say.
In its most recent guidance on highly trusted sponsor status, the UKBA says the scheme will cut red tape for all institutions and will be needed by any institution offering courses below degree level.
This could affect many of the language schools and A-level colleges that act as "feeders" to universities, cutting the flow of students who come to the UK to take lower-level courses and stay on for degrees.
Dominic Scott, chief executive of the UK Council for International Student Affairs, said universities would see the scheme in its current form as a "sword of Damocles" that, if withdrawn, could "damage their reputations" internationally.
Most international students "won't understand that all this was about immigration compliance; they will think it is about the quality of the course," Mr Scott said.
The UKBA said it was bound by pre-election "purdah" rules and could not comment.
The Labour Party said the visa reforms would tackle "the immigration abuse and reputational damage caused by bogus colleges and bogus students".