It was the first time since records began a decade ago that the rate had crept above 30,000, fuelled by an increase in the overall student population.
The rise – in data published by the Higher Education Statistics Agency – comes despite the Government spending £1bn on initiatives designed to improve student retention.
The University and College Union warned that the drop-out rate would soar in coming years following a decision to increase the cap on student tuition fees to £9,000.
Sally Hunt, the UCU general secretary, said undergraduates would be tempted to chase places on the cheapest courses, even if they fail to fit their requirements.
“Over the past five years, in England alone, over £1bn has been spent on measures to improve student retention in higher education,” she said.
“Sadly, today’s figures show that too many students, particularly from disadvantaged backgrounds, are still failing to complete their studies.
“We have real concerns that the new funding regime with hugely increased tuition fees may force some students onto courses that, although cheaper, do not best suit their abilities.
“That scenario is likely to lead to further drop outs, which will not benefit the student, the university or society.”
Figures from HESA show the number of students dropping out of university each year along with the proportion expected to complete the degree they started.
In all, 8.6 per cent of students quit higher education after 12 months last year compared with 7.9 per cent a year earlier. Some 21.6 per cent are expected to fail to complete their degree.
According to data, the worst performer was Highlands and Islands where 32 per cent dropped out last year and just 48.6 per cent of students are expected to finish the degree course they started.
More than one-in-seven students dropped out of higher education altogether at eight other British universities, including West Scotland, Bolton, West London, London Metropolitan, Swansea Metropolitan, Middlesex, University Campus Suffolk and Salford.
By comparison, Cambridge and St Andrews had the lowest drop out rates last year with just 1.4 per cent of students quitting, following by Oxford at 1.4 per cent.
A spokesman for the Department for Business, Innovation and Skills said: "Although our student completion rates compare well internationally, we want to reduce the number of students who don’t complete their studies.
“We are improving information for prospective students so that they can make more informed choices and we are committee to a better overall student experience."