Charles Clarke has ordered funding chiefs to put the brakes on recruitment to degree courses in the run-up to the introduction of top-up fees.
This week's official deadline for applications for courses in 2004-05 is expected to show another increase in demand for places. Much of the growth is due to increased numbers of school-leavers and improved exam results.
But the trend is likely to be multiplied next year by a rush to enter higher education before fees rise. There was a similar stampede when tuition fees were introduced in 1997.
Mr Clarke, the education secretary, wrote to David Young, chairman of the Higher Education Funding Council for England, demanding a report because he is worried that there may be too little cash to support the extra students in 2005-06.
Fees will be charged from 2006, but the government has promised to introduce grants of up to £1,500 a year from this year.
In the annual grant letter to Mr Young, Mr Clarke wrote: "We would be concerned if faster growth than implied by the planned numbers led to overspending of the student-support budget. We therefore look to Hefce carefully to monitor student recruitment and growth for next year and to report to the secretary of state in good time if there are signs that student numbers will exceed current plans."
But the government has limited the options open to it by confirming the drive to expand universities so that half of all under-30s enter higher education by 2010.
Tony Blair this week said it would be unfair to improve schools and pupil performance only to deny qualified pupils the chance of higher education.
And giving evidence to the education select committee this week, Mr Clarke promised that anyone who gets the right qualifications will be able to go to university.
Mr Clarke could have used the maximum student number - a mechanism to control student numbers - if the government had not scrapped it two years ago. It had been introduced by the Conservatives in 1994 specifically to control public spending on student support after the rapid expansion of the early 1990s.
Data released this week by the Higher Education Statistics Agency show the number of students obtaining a first degree last summer up 2.4 per cent to 3,400.
The number of people studying for foundation degrees has doubled to 24,400 this year. And the government confirmed in its grant letter that 50,000 full-time equivalent places will be available by 2005-06. Total public funding, including tuition fees, will rise from £6.04 billion to £6.34 billion in 2004-05.
Growth pressures will compound the problems faced by Mr Clarke as he struggles to head off a potential vote against the higher education bill by fellow Labour MPs. Both Mr Clarke and Mr Blair this week restated the case for variable top-up fees.
Meeting the parliamentary Labour Party, Mr Clarke ruled out any further concessions to the bill before its second reading on January , when the crucial vote will be taken.
He said the bill ensures that the maximum £3,000 fee cannot be raised above inflation unless both the Commons and the Lords approve. Some Labour rebels are suggesting that the £3,000 cap is included on the face of the bill so that further legislation would be required to raise it by more than the rate of inflation.
Although their numbers appear to be dwindling, the Labour rebels could still command sufficient support to defeat the bill. Reports from Mr Clarke's meeting with the parliamentary Labour Party appeared to show some movement to the government position. It is understood that 20 MPs spoke in favour of the bill, with just four speaking against.
Labour MP Peter Bradley, who had put forward proposals for flat-rate fees with colleague Alan Whitehead, said: "This bill is a radically different measure from the one anticipated, and all the changes are for the better."
Several prominent MPs, including Tony Banks, made it clear during the week that they would support the bill at second reading, while several former Cabinet ministers made it clear that they would not.
But some rebel MPs took exception to a leaked memo from George Mudie, former deputy chief whip, to Labour backbencher Barbara Roche that talks of wavering MPs being "dealt with". One MP commented: "It is bad enough being on a whip's list, even worse being on a former whips list."
Labour whips will also hope support from Conservative MPs, up to ten of whom could abstain or vote with the government. Robert Jackson this week became the first Tory MP to say publicly that he will vote with the government on the bill, having no time for his own party's policy of scrapping all tuition fees.
Mr Jackson said: "I will be voting for the government and seeking to persuade as many of my colleagues as I can to vote with me. I am fulfilling the proper role of a Conservative opposition."