The number of university applicants was up 1.4% this year, raising fears that more students will miss out on a place.
In total there were 647,008 applicants, up 9,235 from last year, according to figures from Ucas.
While UK applications were up 0.8% to 550,147, applications from other EU countries rose 5.8% to 45,727 and applications from non-EU countries increased 4.9% to 51,134.
Aaron Porter, NUS president, said: "Last year over a quarter of a million qualified and ambitious young people missed out on a deserved place at university.
"This year the Government has failed to add to the number of university places, withdrawing a small previously planned rise, meaning we are likely to see an increase in the numbers being denied a place.
"With so many students already missing out on university places, any decision to reduce the number available in order to cover the huge black hole in funding left by the Government's rushed and incoherent policy-making would spell disaster for young people, universities and the UK economy."
Universities and Science minister David Willetts said: "Demand for university places has levelled off after unprecedented applications in 2010.
"We provided an additional 10,000 places last year and universities will again be able to recruit the same number of new students this autumn.
"Going to university has always been a competitive process and not all who apply are accepted.
"Despite this we do understand how frustrating it is for young people who wish to go to university and are unable to find a place.
"We are opening up other routes into a successful career.
"Our reforms will make part-time university study more accessible and we are also investing in new apprenticeship places, with at least 250,000 more apprenticeships available over the next four years."