The findings in a Populus poll for The Times will boost the Education Secretary, Charles Clarke, as he starts a series of meetings with his own backbenchers to try to win them over.

The poll, conducted over the weekend, shows that a majority of the public, including nearly two-thirds of Labour voters, believe that the Government’s proposals for variable top-up fees repayable after graduation are fair. It suggests that rebel Labour MPs are out of step with public opinion. Labour voters are more supportive than either Tories or Liberal Democrats. Moreover, tuition fees are preferred as a means of funding higher education to the Liberal Democrat alternative of increasing taxes or the Tory one of cutting student numbers.

The findings are welcome ammunition to the Government as it attempts to rally support among Labour MPs before the key Commons vote next month on the Bill introducing top-up fees. More than 150 Labour backbenchers have signed a critical Commons motion, double the number required to defeat the Government as both the Tories and Lib Dems oppose the plan.

Mr Clarke last night met with Labour MPs as he and Mr Blair tried to reduce the scale of next month’s rebellion. He told them why the Government had opted for a tuition fees scheme rather than a graduate tax, which several ministers including Gordon Brown originally favoured. Many Labour MPs support the introduction of a graduate tax and have told ministers that their position would change if Mr Clarke looked again at this proposal.

The new poll also shows a firming in Tory support since Michael Howard was elected party leader. But support for Labour has been unchanged for three months running at 36 per cent, while the Tories have risen two points to 33 per cent, with the Lib Dems down three points at 22 per cent.

A majority of Labour voters (55 per cent) back variable fees for different courses, one of the main objections for many Labour MPs.

Nearly a half of Labour voters (44 per cent) back repayable fees, against a third (32 per cent) believing that the costs should be met by raising income tax from 40 to 50 per cent for those earning more than £100,000 a year. Almost two-thirds (64 per cent) think that the Government’s plan “sounds like a fair way to raise extra funding”.

More Tory voters (39 per cent) are sympathetic to the Government’s plan for top-up fees than to their own party’s call for cutting university places (backed by just 11 per cent). A majority of Tories (52 per cent) think top-up fees are fair.

The main public criticism of the proposals is over the suggestion that graduates should start to pay back tuition fees once their income is over £15,000. Two-thirds (67 per cent) of all voters. and nearly three-quarters of Labour supporters (72 per cent) believe that the threshold should be higher. However, senior ministers have already hinted at concessions.

The poll shows that professionals, managers and graduates are more hostile to repayable top-up fees. Among those who finished their education over the age of 19, that is graduates, more favour higher taxes than repayable fees (by a 44 to 32 per cent margin). The figures are exactly reversed for those who finished their education between 15 and 18. Moreover, graduates are evenly split on the merits of variable fees and they are even keener than other voters to raise the repayment threshold.

However, the poll shows that a majority of all groups of voters is hostile to the Government’s target of 50 per cent of the 18 to 21 age group going into higher education.

Mr Clarke gave MPs a six-page document explaining the case against a pure graduate tax. He said that the fees plan contained many of the fairness principles of the graduate tax. Both required graduates, not students, to pay towards their higher education; both linked repayment to earnings; and both meant that if a graduate did not work they did not pay.

Populus interviewed a random sample of 1,006 adults aged over 18 by telephone between December 5 and 7.

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