LONDON (Reuters) -- Several thousand students converged on Trafalgar Square in central London from all parts of Britain on Sunday to demonstrate against higher university tuition fees.

Police put their number at around 3,500.

The National Union of Students (NUS) said the introduction of fees -- which mean students have to pay up to 3,000 pounds a year towards tuition costs -- had resulted in a fall in applications.

The student body wants the government to reverse its policy of making undergraduates pay the top-up fees.

Figures from the university admissions system, UCAS, showed that about 15,000 fewer students began courses this September than last year.

The 3,000-pound charge applies to students who started courses this September.

"The decision to go to university is becoming an increasingly hard one to make," said NUS National President Gemma Tumely.

"Weighing up the prospect of graduating with huge levels of debt and starting on an average salary of just 19,000 pounds is difficult. It is clear that admission for some students is proving impossible," she said in a statement. "Alan Johnson, the education and skills secretary, has said publicly that if top-up fees deter students from low-income backgrounds, he would consider 'abandoning the policy altogether'."

The government says the new system is fair and reflects the fact that most students gain better-paid jobs on graduation than people who enter the workforce straight from school.

Students do not have to repay the tuition costs until they leave university and start earning money.