More than half of vice-chancellors fear that first-year students lack the basic skills needed to study for a degree, according to a survey by the Conservative Party.
Fifty-four per cent of vice-chancellors who responded raised concerns about the mathematical abilities of students on technical courses for which a high level of mathematical knowledge is required.
Two-thirds of vice-chancellors said they had to provide classes in numeracy to bring students up to speed.
Chris Grayling, Shadow Higher Education Minister, said: "Universities are being asked to pick up the pieces caused by failings in the school system.
"Universities should be able to be confident that students arriving to do maths and technical courses are well equipped to do those courses. They should not have to use scarce resources to teach school-level maths."
The Tories report that one vice-chancellor told them that he had been forced to set up a special "mathematics support centre" to address the problem. Another reportedly said: "We in universities now have to teach basic maths in the first year."
A third said: "Numeracy has been a particular issue for us, primarily in relation to areas of science and engineering."
The results were released to The Times Higher as a prelude to the party's long-awaited higher education policy. The policy, due to be announced by leader Michael Howard before the parliamentary recess on July 22, will include a plan to halt university expansion.
The party's proposals will include the abolition of tuition fees and the abandonment of the Government's target to get 50 per cent of all 18 to 30-years-olds into higher education by 2010.
Mr Grayling said: "It makes no sense to move to a 50 per cent participation rate when universities are having to tackle these issues among their current intake."
Mr Grayling said the vice-chancellors survey also revealed the damaging effects of funding shortfalls. Half the respondents said that they either had recently considered or would be considering in the near future the rationalisation of some departments or course provision.
Chemistry and other science-based courses, engineering and modern languages were most commonly cited as candidates for rationalisation, he said.
Mr Grayling said that the party would produce detailed proposals to increase university funding beyond simply relying on a contraction of student numbers.
This has raised speculation that the Tories will resurrect their 2001 manifesto plans to fund universities through endowments.
- The Government this week defended the "vital role" of two separate inquiries into post-14 education as it emerged that they have cost the taxpayer £1.5 million, writes Paul Hill.
In answer to a parliamentary question, David Miliband, Schools Minister, said that the inquiry into 14-to-19 curriculum reform by Mike Tomlinson, the former chief inspector of schools, had cost £1.1 million. The separate inquiry into mathematics post-14, by Adrian Smith, principal of Queen Mary, University of London, had cost a further £400,000.