The coalition government is expected to face the largest show of opposition to its austerity cuts since it came to power when tens of thousands of students take to the streets today to protest against increases in university fees.

Some 24,034 students have registered to take part in the march, and many have purchased seats on coaches booked to ferry students to central London.

The largest student contingent is expected to come from London-based universities, which are anticipating more than 5,000 marchers to show up. About 3,200 students from other universities in the south-east have said they will attend, with more than 4,500 students signed up from the West Midlands, Yorkshire and Humberside. The march is organised by the National Union of Students and the lecturers' union, the University and College Union (UCU).

Fourteen coaches have been booked to bring about 700 students from Manchester's two universities alone and 600 students from Reading University have said they will attend.

A big delegation is expected from Sheffield, where activists say anger has been directed at the deputy prime minister, Nick Clegg, whose constituency is in the city. He has been widely criticised for reneging on a Liberal Democrat election promise not to increase fees.

Students put calls out on Twitter and Facebook to make Clegg's west London home the target of a spontaneous "flash mob" rally on the eve of the march. Aaron Porter, the NUS president, said: "This is the largest student protest in the UK for at least a decade … which goes to show the huge extent of discontent with this government's short-sighted plans, which will effectively privatise large parts of higher education and remove support for many college and adult education learners."

Students with a track record of running "direct action" campaigns are also known to be planning co-ordinated sit-ins and occupations alongside the march.

The Metropolitan police, which is thought to be expecting 15,000 protesters, said it had been in discussions with the NUS and other groups planning to march along the Embankment.

Meanwhile, in a letter to the Guardian , nine university vice-chancellors warn the government that it is making a "profound error" by withdrawing public funds from undergraduate teaching.

They argue that government proposals to raise tuition fees to as high as £9,000 and make deep cuts to teaching budgets "assume that higher education is of value only to the individual but not to society or the economy". Although students will not be required to pay fees upfront, the fear of debt will deter the poorest, the vice-chancellors believe.

Professor Caroline Gipps, vice-chancellor of Wolverhampton, said: "I do think that many of the sorts of families that we work with will think very carefully before they take on this level of debt. That [level of fees] is a tall order for families that don't have a lot of income, don't have a history of going to university."

Many of the universities that have signed today's letter have a high proportion of ethnic minority and working class students. The University of East London had 4,590 black students in 2007/08. By contrast, the entire Russell group of 20 highly selective universities had 7,815 black students.

Research published by the UCU shows the annual cost of a degree has risen by 300% in two decades. It says the cost of going to university to a graduate from an average household in 1988-89 was £1,545.50. This had risen to £6,360 by the latest academic year. By 2012 – the year the new tuition fee cap is due to be introduced – the union suggests that the annual cost for fees and maintenance will be £12,750.

The analysis claims that, in comparison with the increase in the cost of going to university, the cost of a shopping basket of everyday items rose by 127.1% between 1988 and 2010.The union also claims that, despite increasing costs, the staff-to-student ratio has risen, with one member of staff for every 16.3 students in 2008-09, up from one staff member for every 12.6 students in 1988. Yesterday the universities minister, David Willetts, corrected last week's statement on student support by revealing that students from households earning between £49,000 and £53,000 will receive, on average, £120 less in maintenance loans than previously stated.