The overspend for the current year is thought to be in the millions though the final figure is still being worked out by the Further Education Funding Council.

There was considerable surprise two years ago when ministers signed what was seen as “an open cheque” for colleges which increased student enrolments beyond the FEFC’s targets.

While full-time equivalent students recruited up to a college’s target brought in around Pounds 2,000, any more earned it Pounds 750. There was no limit set on the number of extra students colleges could recruit and this has created the overspend.

The money was too little to encourage colleges to cheat and set artificially low targets. But for those who could benefit from economies of scale, or had surplus capacity on courses or were low spenders, it was soon seen as a lucrative source of extra cash.

Evidence of the overspend is certain to lead to Treasury demands for more detailed efficiency measures in the run-up to the public spending round this autumn. But it is difficult to see how they can halt the cash-flow which they have agreed for at least the next two years.

A senior official at the Department for Education and Employment told The TES: “When the Treasury agreed to the funding formula, ministers were confident that colleges which overshot targets would be outweighed by those which fell short. This clearly has not happened.”

It is reminiscent of what happened in higher education when the Treasury agreed to fund without limit “fees-only” students, provided universities and colleges absorbed other institutional costs. As with FE, it was seen as a good way of driving down average costs while expanding. The HE students, however, were also entitled to grants, and the bill mushroomed.

A complex funding formula was drawn up by the FEFC during consultations with principals when FE and sixth-form colleges left local education authority control in 1993. It aims to promote efficiency, eliminate extreme differences in spending inherited from LEAs - there was a seven-fold difference between the highest and lowest spenders - and to encourage 25 per cent growth in student numbers over three to four years.

Payments are also made to discourage drop-outs, and to make colleges more responsive to the needs of students and employers.

Given the diversity of colleges, their mix of full-time and part-time students and the range of course costs, this method of funding by full-time equivalent student numbers was seen as unfair. Now each student is worth a certain number of financial “units”, depending on the cost of their courses. For example, engineering would have more units than an A-level English course.

Colleges can claim additional units if they waive tuition fees for the unemployed, provide child-care facilities for students in need or run special programmes for people with learning difficulties and disabilities.

Students recruited above the agreed targets now earn the college Pounds 6.50 per unit. And the flexibility of the new formula that allows colleges to recruit yet more students has increased demand again.