The University and College Union (UCU) claims that the move will eliminate unconditional offers and the “chaotic” clearing process.
A report, Post-qualification Application: A Student-centred Model For Higher Education Admissions in England, Northern Ireland And Wales, published today, suggests how the admissions system could be overhauled.
Under the proposal, students would apply to university only after finding out their exam results and start the first year of their higher education course in November.
According to the UCU, the reforms would make the system fairer, and bring the UK into line with the rest of the world.
It says no other countries use predicted grades to award university places, and seven in 10 staff involved in university admissions back the move to post-qualification application.
Ucas figures show that in 2018 more than a third of 18-year-olds applying to university received a form of unconditional offer before completing their school qualifications.
The report also looks at how to improve advice for students when it comes to deciding what to study, and calls on the Government to commission a review of university admissions.
UCU head of policy Matt Waddup said: “There is growing support for a shift to a system where students apply to university after they have received their results. This report sets out how that could work in practice.
“Such a move would not only be fairer for students, it would bring the UK into line with the rest of the world.”