By Mike Baker BBC education correspondent

Visitors from abroad and trouble with the domestic staff must have made it a trying few days.

But next week could be worse.

When she opens the new session of Parliament on Wednesday she will have to announce her government's somewhat unpopular plans for higher university tuition fees.

The plans intend to create a pseudo-market in university tuition fees, with each university allowed to charge undergraduate fees of up to �3,000 a year.

Most of the opposition to the plans has come from those shocked by the increase in fees, which could almost triple in cost from the current �1,125 a year.

They fear this will deter those from poorer backgrounds from entering higher education.

Up-front fees abolished

Other elements of the plans have received less attention but are just as significant.

It is perhaps surprising that the government, until recently, has not made much of this point

The first is the change to a deferred payment scheme. At present it is a "pay-as-you-go" system: the student, or very often the parent, contributes while they are still studying.

Under the proposed system, payment becomes due only after the student has graduated, found employment, and started to earn at least �15,000 a year.

In other words, university once again becomes free at the point of use, taking us back to before 1998 when the current fees were introduced.

It is perhaps surprising that the government, until recently, has not made much of this point when trying to "sell" the policy.

Indeed, this deferred payment system might have been dressed up by the "spin doctors" as an interest-free loan, worth up to �9,000 over a three-year course.

It could certainly be interpreted as good news for parents. While many mums and dads feel they should now pay the fees for their 18- or 19-year-old student offspring, will they still feel obliged to pay for them when they are in their mid-20s and in work?

Poverty gap

The other change in the payment arrangements may be harder to sell.

At present tuition fees are means-tested. Students whose parents earn less than �20,000 a year pay nothing.

Students again demonstrated against tuition fees last month

So currently about 40% of students are fully exempt from fees with a further 20% receiving partial exemption.

But under the new plans, the fee exemption will be available only on the first �1,125 of tuition fees.

So a student from a poor home who currently pays no fees may, if they go to a university charging the maximum, be �1,875 a year worse off.

There is help for the very poorest as the government is reintroducing grants of up to �1,000 a year. However only those whose parents' eligible income is below �15,000 will receive this grant.

Yet even the maximum grant and maximum fee exemption (a total package of �2,125) will still leave the poorest students �875 short of the fees likely to be charged at leading universities.

Strictly speaking, of course, this debit and credit calculation is only true in the long term, as no student pays any fees until they have graduated and started to earn.

Nevertheless, it can look like a raw deal for the those from the poorest homes.

Bursaries

Which is why the government is talking up the role of new student bursaries. These are likely to be funded out of the tuition fees collected by universities.

One issue will be the reaction of better-off students and parents when they realise their full-rate fees are being used to subsidise others

It has been suggested that about one-third of fee income might go towards funding bursaries.

And this is where its starts to get potentially troublesome.

One issue will be the reaction of better-off students and parents when they realise their full-rate fees are being used to subsidise others.

The subsidised student from a poorer home may then go on to a highly-paid job in the City and earn millions, while the student from the more affluent home may take up a low-paid, public sector job.

There is also the added complication that some universities will have to fund far more bursaries than others since the distribution of students from poorer homes is far from equal at our universities.

Indeed those universities which will most need to provide bursaries will be the very ones which will find it most difficult to charge the maximum level of fees.

Central pot

One suggestion to resolve this has been the creation of a national bursary scheme.

This would mean all universities paying into a central pot which is then distributed to students on a needs-based assessment.

Not surprisingly this has not proved popular with leading universities - the very ones who say they most need higher fees in order to compete internationally.

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They will hardly think it has been worth all the pain of raising fees if they see a substantial amount of that extra income being distributed to students at other institutions.

The other element of the new system which has, perhaps, not yet been fully appreciated is that it will create a market system for higher education.

This has been underplayed because universities have, understandably, been reluctant to say how much they will charge if the legislation does go through.

US example

It has been assumed by many that most of the leading universities will charge the maximum �3,000. This seems likely.

Few will want to risk their courses being seen as second-best because they have a "bargain" price label stuck on them.

Nevertheless, there may well be some universities which stick with the current fee levels (in theory, some could even cut fees to zero, although this seems unlikely).

What will this differential pricing mean for student choice? It is hard to predict but there is one model: the USA.

American universities have very different fee levels. The private universities, like Yale and Harvard, cost tens of thousands of dollars a year.

Public universities are much cheaper but still show wide variations. For a leading public university fees equivalent to �4,000 to �5,000 are typical.

But that is only half the story.

Limited choice

The states which provide part of the funding for public universities want to make sure that they are not subsidising students who come from other parts of the country.

So, while "in-state students" may pay �4,000 to �5,000 a year, those who come from out of state might pay double or triple that amount.

Not surprisingly, the great majority of American students go to their local university, whether or not it is the "right" choice for them

The universities may not feel this is fair but - in many American states - the governor can limit fee levels.

They often do so. After all, protecting the fees of local students tends to be popular with local voters.

So, even in the USA, the market in university fees is not a free market. Indeed I can think of no country where there is a free market in university tuition.

One effect of the distortion in the USA is to limit student choice.

If you live in Chicago, for example, you will be under greater financial pressure to go to the University of Illinois, where you will pay in-state fees of about $7,000 a year, rather than going to the University of Michigan, where you will pay more than three times as much as an out-of-state student.

Not surprisingly, the great majority of American students go to their local university, whether or not it is the "right" choice for them.

Will pricing have a similar effect in England? Will students pick a cheaper, former polytechnic which is charging, say, �1,500, over an elite institution which is charging double that?

The American experience, while not exactly comparable, suggests they might.

When the Queen fires the starting gun on the new session of Parliament, we can expect these arguments - and many more - to dominate the politics of higher education for many months ahead.