The government wants excellence, access and relevance within existing budgets. The first problem it faces is to define which students and qualifications count as higher education.
Prime minister Tony Blair inadvertently created the problem when he announced at the Labour Party conference in 1999 his target of 50 per cent participation for 18 to 30-year-olds by 2010.
There is no adequate definition of which students aged between 18 and 30 and which qualifications count towards the initial entry rate (IER) to higher education.
The rate measures those starting a higher education course for the first time. It is currently about 40 per cent, according to the Department for Education and Skills.
Higher education minister Margaret Hodge said: "We need to define what we mean by participation. We are working on this definition to find out what counts as higher education."
A focal point is the interface between higher and further education. Confusion here undermines government's aim to make it easy for learners to progress smoothly from school to college to university.
One difficulty concerns level-four and level-five national vocational qualifications, nominally equivalent to degrees and higher degrees. These count towards the IER. The same is true of sub-degree higher national diplomas and certificates as well as the new foundation degrees.
But NVQs and related vocational qualifications are funded by the Learning and Skills Council and not by the Higher Education Funding Council for England. HNDs, HNCs and foundation degrees are funded by Hefce.
A spokeswoman for the DFES said that Hefce had no plans to take over the funding of NVQs. But she said that the funding council took on funding for HND and HNCs "with the intention of extending this to all higher education programmes accredited as higher education level by the Qualifications and Curriculum Authority".
By 2003, the QCA should have accredited NVQ and vocationally related programmes submitted by colleges and exam bodies. It is currently assessing the level at which these qualifications should be offered and is working with the Quality Assurance Agency to ensure comparability between the academic and vocational streams.
Ms Hodge is determined to achieve parity of esteem between vocational and academic awards. This may prove challenging while qualifications of comparable level are funded by different bodies. Furthermore, NVQs and other vocational qualifications are quality-assured by the Adult Learning Inspectorate, not the QAA.
Education ministers want more collaboration between schools, colleges and universities to increase higher education opportunities for poorer people. Simplification of higher vocational structures is key to ensuring collaboration.
Already, 40 per cent of people in higher education come from further education colleges. Collaboration and rationalisation of the academic and vocational routes could increase this proportion.
The government will be keen to exploit the inbuilt gearing between the two sectors. The further education sector has over 4 million students compared with just over 1 million in higher education. A modest increase in college students going on to university would have a significant impact on higher education entry rates.
Colleges' success in widening participation means that higher education entrants from further education are more likely to be the the students the government wants - those from poorer and disadvantaged backgrounds.
Many in further and higher education see huge problems in expanding the IER to 50 per cent.
One of the thorniest problems is student support. Ministers, including Tony Blair and Gordon Brown, agree that whatever is devised should not deter people on grounds of cost.
But what the DFES, Downing Street and the Treasury cannot agree on is how this should be achieved. Graduate tax and loans bearing real interest rates are two options. What is not clear is if this will mean more money overall for students.