The process by which hundreds of thousands of teenagers apply to UK universities favours the rich, the organisation that co-ordinates degree applications has admitted.

In a review of university admissions published on Monday, Ucas acknowledges that the current system gives an unfair advantage to pupils at private schools. These pupils are encouraged by their teachers to apply to institutions well ahead of the official deadline and, for some courses, applying early gives students more of a chance of being offered a conditional place, the review admits.

At present, too many pupils have to apply to universities before they have had time to properly research what and where they want to study, Ucas argues. This favours students whose families are familiar with the university application process and puts the rest at a disadvantage.

The current system also assists pupils whose schools employ tutors who are very familiar with the university applications process, and do not feel intimidated about phoning up an admissions tutor to plead the case of a particular student.

Ucas, backed by the entire education establishment, is calling for the government to make the most radical overhaul of university admissions for 50 years.

It argues that teenagers should no longer apply to university with predictions of what they will achieve in their A-levels, but instead only submit their applications once they have their final grades.

This would involve teenagers sitting their A-levels and equivalent exams 15 days earlier and exam boards handing out their results at the end of the summer term, rather than in August. Students would then apply to university with their results in July.

They may only be able to apply to two institutions. At present, they can apply to up to five. Those who do not receive any offers could reapply straight away. Clearing – the process by which students without offers are matched with universities with vacant places – would be abolished.

Universities would have to tell students whether they have been accepted in late September or the beginning of October.

One option under consideration is to have a single date on which universities tell students whether they have been offered places and on what conditions. At the moment, students hear from universities on different dates up to the end of March. Ucas said the proposals could be in place by 2016.

The Guardian was first to reveal the plans, which were set out in a presentation by the head of Ucas at a closed meeting with vice-chancellors last month.

The Department for Education said the proposals would mean "big changes" to the timetable for A-levels and the way they were taught and marked. "We need to consider carefully the impact ... on everyone involved, especially pupils," a spokesman said.

Universities were tentatively supportive of the plans, but warned that they did not just judge applicants on their grades and needed time to assess their overall talents. Wendy Piatt, director general of the Russell Group, which lobbies for the 20 leading universities in the country, including Oxford and Cambridge, said she was concerned that the proposals "might restrict the ability of institutions to make a fair and thorough assessment of applicants".

One of the major teaching unions, the Association of School and College Leaders, said the changes would require effort and adjustment from all those involved in education, but would be in the best interests of young people.

Labour sought for years, without success, to bring in similar changes, but was forced to abandon the plan in 2006 when teaching unions and others rebelled.

"Giving applicants from families where there is not a tradition of university an extra six to 10 months to mature, learn more about their preferred higher education institutions and prepare applications would encourage more confident and informed applications," the review says.

Some applicants, "particularly younger learners at independent schools, are often advised to apply early in order to maximise their chances ... There are indications that for some courses acceptance rates are higher for earlier applicants". There is an "undesirable divide between those applicants who receive effective advice and those who do not", it adds.

Ucas argues that the current system forces applicants to make choices about where and what to study six months before they receive their exam results, which is too early.

It believes predicted grades are unreliable. Research conducted by Ucas for the government shows that just 52% of predicted grades are correct and fewer than 10% of students have three correct predicted grades.

The review says the current system was not set up for the growing numbers of overseas students who apply with a wide variety of qualifications, nor for applications from mature students who want to study part-time and start their courses in January, rather than October.

"We have a system that lacks transparency and is inefficient for many applicants and is cumbersome for higher education institutions," the review says.

Ucas will be consulting on the plans between now and 20 January.