It is important that students from a disadvantaged background are not put off attending university.
The Association of School and College Leaders (ASCL) warned that although it is important to invest in higher education, it is vital that university remains accessible.
"Schools and colleges have put a lot of energy and effort into raising the aspirations of all young people and they strongly support the notion that all who would benefit should be able to access higher education," said ASCL general secretary Brian Lightman.
He noted that it would be "dreadful" if young people are deterred from attending the country's best universities because of the cost of courses.
"We do not want an open market in university fees discouraging less well off students from reaching their full potential," Mr Lightman commented.
Published today (October 12th), Lord Browne's review into higher education recommends that institutions be allowed to lift tuition fee caps.