The heads of elite universities were awarded an average pay rise of £9,700 last year, taking their average earnings beyond £333,000, the Guardian can reveal.

Analysis of 13 top university leaders' pay packets has prompted calls for the prime minister's clampdown on executive pay to reach beyond banks and big business to include universities as well, although the average rise of 3.9% is below the rate of inflation.

An examination of the universities' most recent financial statements, from 2010-11, shows the vice-chancellors of Oxford, Cambridge, Birmingham, Edinburgh, Leeds, Nottingham, Bristol and Southampton were all given a pay rise, despite a squeeze on many university budgets.

The most highly paid of the 13 was Oxford University's Professor Andrew Hamilton, who received a pay packet of £424,000. This was made up of a £371,000 salary and £53,000 in pension contributions.

Hamilton was closely followed by Birmingham University's Professor David Eastwood whose earnings reached £419,000, comprised of a £323,000 salary, £29,000 bonus, £16,000 for other expenses and £51,000 for pension contributions.

The 13 universities whose accounts the Guardian analysed are members of the Russell Group, a 20-strong group of research-intensive institutions.

Sally Hunt, general secretary of the lecturers' trade union – the University and College Union – argued that the findings meant the government's crackdown on excessive executive pay should extend to universities.

Last week, David Cameron announced that he wanted to push through legislation to curb exorbitant boardroom pay and said that it made "people's blood boil".

All three of the main political parties are vying to lead calls for a crackdown on executive pay. In the past financial year, the directors of FTSE 100 companies have seen a 49% increase in total earnings, taking average pay to £2.7m.

Hunt said an average pay packet of £333,000 was "eye-wateringly high" particularly because, since 2009, lecturers have had a 7% real-terms pay cut. The median pay of a university lecturer in 2011 was £45,364. The increase in median pay for full-time lecturers between 2009-10 and 2010-11 was 3.7%. Hunt called for university staff to sit on the remuneration boards that decide vice-chancellors' pay and pensions.

Most universities have remuneration committees that decide on the vice-chancellors' pay packet. The committees do not often include employees and tend to keep their discussions private.

"I think there is a very strong argument, especially in light of the current clampdown on executive pay, for employee and student representatives to sit on university remuneration boards," Hunt said. "It is vital that we ensure there is proper scrutiny of vice-chancellors' pay and pension provision if we are to avoid suspicion of one law for those at the top and another for the rest."

Usman Ali, the National Union of Students' vice-president responsible for higher education, said students struggling to make ends meet and facing record youth unemployment would find the prospect of "university fat cats lining their pockets even further utterly sickening".

The rector of Imperial College London, Sir Keith O'Nions, was the third highest-paid vice-chancellor of the 13 with a pay packet of £354,000, of which the salary was £296,000.

Eastwood had the highest rise in his pay packet – a 7% rise compared with the previous year. Southampton, Nottingham and Cambridge universities raised the amount they spent on their vice-chancellors between 2010-11 and 2009-10 by 3.4%, 3.3% and 3.6% respectively.

The increase in the vice-chancellors' pay packets at Oxford, Leeds, Bristol and Edinburgh universities was less than 0.5%.

While the vice-chancellors were receiving higher pay packets than the year before, university budgets were being cut. In 2010-11, around £215m was shaved off teaching budgets – the equivalent of a 1.6% real-terms cut. The amount given to capital projects, such as new buildings, was cut by 14.9% in cash terms – a £142m cut.

However, the annual reports do show that some vice-chancellors took pay cuts. Imperial College's O'Nions, Liverpool University's Sir Howard Newby and University College London's Professor Malcolm Grant all took a cut.

The accounts also reveal a growing number of university staff are being paid more than £270,000. At Imperial College London, six employees were listed as earning £270,000 or more in 2010-11, compared to three the year before.

At Liverpool University, four staff were on £270,000 or more, compared to just one the year before. At Oxford and Cambridge, four staff came into this pay bracket, compared to three the year before.

Our analysis also shows that Cambridge University was £10m in deficit last year – unlike several other of the 13 universities which reported record surpluses. The deficit was on continuing operations after depreciation and before tax. Cambridge decided, despite the deficit, to award its vice-chancellor, Professor Sir Leszek Borysiewicz, a pay packet of £258,000, which included £35,000 in pensions.

The annual report states that Cambridge's internal analysis suggests that the university is "falling behind key competitors in realising external research grant funding".

It adds: "Work is therefore under way to establish strategic research initiatives which will provide a framework on which to build major bids for funding. Work will also be undertaken to establish why funding from business-based activity remains low, particularly given the university's reputation for hi-tech activities."

Meanwhile, Oxford made an £11.4m surplus, while Manchester, Edinburgh and Glasgow made record surpluses of £54.1m, £43.7m and £9.8m respectively.

Nicola Dandridge, chief executive of Universities UK, the umbrella group for vice-chancellors, said the remuneration packages "reflected what it takes to recruit and retain individuals able to run complex, multimillion-pound organisations, which are operating in an increasingly competitive, global market".

"Across the sector there have been very few increases, reflecting the current funding climate," she said. "These levels are in line with our competitor countries and also with heads of public and private organisations of a similar size."

The table below shows the pay packets of top university leaders by year and institution.