It was a rash promise, made amid the euphoria of a general election victory - and it has proved much harder to deliver than to make.
At the post-election Labour party conference in October 2001 the Prime Minister promised to look again at the way degrees were funded, and "find a better way to combine state funding and student contributions". A short, sharp review was promised. But over a year later, and after a change of Education Secretary, everyone is still waiting.
The review began because Labour canvassers had been given a hard time on the doorstep over the party's introduction of degree tuition fees.
Now, as the Government desperately scours the world for alternative funding models, many insiders believe Blair should never have re-opened the issue. They argue the Government had weathered the storm over tuition fees; all that was needed was a gradual increase to the pound;1,100 means-tested fee.
It is too late for that now. The review started with ideas for a graduate tax, moved on to so-called "top-up" fees (effectively much higher tuition fees), and now seems to have come almost full circle. What started out as a proposed Green Paper became a proposed White Paper but, with the onset of political nervousness, has been demoted to a mere "strategy paper" that will give the Government maximum room to change its mind.
Why has it all proved so difficult? The root of ministers' problems is that they have two conflicting aims. On the one hand, they are committed to increasing the numbers going to university and, specifically, to attracting more from poorer backgrounds. On the other hand, they are determined that the extra money needed to expand universities, and to allow the best to compete internationally, can no longer come from general taxation.
So the Government wants to attract more students from poorer homes yet also wants a student body that will on average be poorer to contribute more to the cost of degrees.
Most of the pressure for change has come from a few leading universities and the Downing Street policy unit, led by Andrew Adonis. Indeed in mid-autumn they appeared to have done a deal to introduce "top-up fees". A paper was ready when Estelle Morris resigned.
But then Imperial College, London, rocked the boat. It talked of charging undergraduates up to pound;10,500 a year. The media scented a story, the middle classes were duly petrified and anxiety that huge upfront fees would be a political disaster spread through the Cabinet.
As ministers look at the options, there is one thing they cannot ignore: the need for an urgent injection of cash for universities. Ministers acknowledge that funding has failed to keep pace with breakneck university expansion.
In just 20 years, we have moved from one in eight school-leavers entering higher education to one in three. Add those who go to university later in life and the proportion of 18 to 30-year-olds entering higher education has risen to 41.5 per cent.
University vice-chancellors say they need at least pound;10 billion in the next three years. But ministers believe the taxpayer cannot pick up this entire bill. That is why either students, parents, or graduates face paying more.
So what are the options? The first choice is between a flat-rate fee or a deregulated system where fees vary by institution and course.
If ministers stick to a flat-rate fee, it will have to rise substantially to bring in enough income. Forty per cent of students pay nothing as their parents' combined income is less than pound;20,500. A further 20 per cent pay reduced fees. Assuming means-testing stays, the burden on the middle classes would have to rise sharply.
A more radical option is to require everyone to pay the full fee. But this could only be done alongside other reforms, such as increased loans or the return of means-tested grants.
The deregulated fees approach is effectively the same as top-up fees, but ministers could limit the impact on middle-class wallets by capping the fee each university could charge.
The next choice is between upfront payment at the start of every academic year, and deferred payment. The problem with paying upfront is it will deter poorer families and anger middle-class ones, who can afford to pay, but do not want to. For these reasons, ministers seem to have abandoned plans for big upfront fees. Instead the search is on for a deferred payment scheme or a hybrid scheme like the one in Australia.
The Australian Higher Education Contribution Scheme (HECS) gives students a choice between paying fees upfront, with a 25 per cent discount, or later through the tax system once their annual earnings reach around pound;8,300.
The discount may seem unfair on those who cannot afford to pay upfront but financial experts say inflation makes it cheaper overall to pay later. Under the deferred payment option, students are loaned the fees and pay the debt off after graduation. The rate of interest is equal to inflation, meaning the debt is interest-free in real terms.
Fears that HECS would deter poorer students have proved unfounded, says Professor Gavin Brown, vice-chancellor of Sydney University.
However, Professor Brown points out that, as fee income has grown, state funding has been pared back. Some leading Australian universities are now pressing for extra upfront fees in addition to HECS.
It is a fair bet that the coming strategy paper will propose something like the Australian model, although it may allow variation in the fees universities can charge and propose a limited return of grants for poor students.
But deferred payment will not deliver the urgent cash injection universities need. Ministers will still face a 'black hole' in university funding as a deferred scheme will not bring in much money for over a decade.
However, savings could be made elsewhere. Professor Nicholas Barr of the London School of Economics says scrapping subsidised rates of interest on student loans could free up pound;800 million a year for universities. He argues students should get a loan big enough to cover all fees and living costs. This would not only save the state money but end the deterrent effect of fees as degrees would be 'free' at point of use. Graduates would pay the loan back on an income-contingent basis.
The package of measures is likely to be complex and will include several options. The Government knows it must get this right or it will lose middle-class votes.
Whatever the solution, it will not please everyone. Ministers are left wondering if they should have just spun their original solution - means-tested tuition fees - better. As one minister told me: "Our big mistake was calling them 'fees', if we had talked about 'student contributions' instead it would have been so much easier to sell."
Mike Baker is the BBC's education correspondent.