Meanwhile, the Russell Group has argued that universities with a proven track record of passing quality reviews should be reviewed only once a decade.
These are among the official submissions to a Higher Education Funding Council for England consultation that canvassed the sector on plans for a risk-based quality assurance system.
Under the plans, the Quality Assurance Agency's scheduled full institutional reviews could from 2013-14 fall in frequency from their present level of about one every six years.
The consultation, which closed on 31 July, proposed two routes for monitoring and review: a more frequent Route A for providers that have not yet successfully undergone two external institution-wide reviews (principally further education colleges and private providers); and Route B for those that have undergone two such reviews (universities).
In its consultation response, the Russell Group says a gap of 10 years between full audits "should be available for universities on Route B which are comfortable with such an arrangement, because these institutions have a track record of successful QAA review".
The new quality assurance regime "should aim to achieve very substantial deregulatory change for institutions able to demonstrate low risk", it adds.
However, the Million+ group of new universities says the interval should be kept at six years.
Institutions could change significantly in a decade and effective reviews were central to maintaining the "international reputation of UK HE", it says in its response.
Hefce's consultation document dropped the government's suggestion - made in last year's higher education White Paper - that institutional review could be scrapped for some universities, a suggestion the Russell Group is thought to have supported.
Instead, Hefce proposed that the interval between reviews should be between six and 10 years and sought views on the right frequency.
However, Hefce cautioned against an interval of 10 years, noting that this could leave English universities outside important European quality assurance standards.
In line with the White Paper, the consultation also outlines plans for out-of-cycle QAA investigations to be triggered by clusters of complaints from students and by annual data reviews - potentially including National Student Survey scores.
The 1994 Group says in its response that "the sector should only support a move to a longer cycle if it is clear that the 'triggers' for ad-hoc interventions are sufficiently robust".
The University Alliance outlines risk factors that it believes should trigger reviews, including a change of ownership or a merger; "significant new collaborative provision" to avoid validation scandals such as those that brought down the University of Wales; "significant negative press and media attention"; and "a petition from 30 or more per cent of the student population".
It also says in its response that 10 years would be "too large a gap" between full reviews and might "increase the risk to the sector's reputation".