The authors of a report which claimed that state school students achieved better degrees than those from private schools have admitted getting their numbers wrong.

The Higher Education Funding Council for England (HEFCE) said in September that in 2013-14, 82 per cent of state school leavers who graduated from English universities achieved a first or a 2:1, compared with 73 per cent of independent school students.

In fact, the reverse was true. This was, HEFCE said, down to a “transposition error”.

The error was pointed out by the University of Buckingham’s Centre for Education and Employment Research (CEER).

Professor Alan Smithers, director of CEER, said: “It is extraordinary that an influential body like HEFCE should have got its figures wrong.”

A spokeswoman for HEFCE said: “We made a transposition error in our latest report on degree outcomes which we’ve corrected on our website and in social media. In 2013-14, 73 per cent of state school graduates gained a first or upper second-class degree compared with 82 per cent of independent school graduates.”

Despite the mistake, HEFCE stressed it did not affect the main finding of the report which was that: “For all but those with the very highest A-level grades, state school graduates tend to have higher degree outcomes than independent school graduates with the same prior educational attainment.”

It added: “The nine percentage point difference in favour of independent schools is explained by the different distribution of A-level achievement between state and independent school graduates - independent school students, on average, achieve better A-levels than state school students.

“When this and other known factors (such as degree subject) are taken into account, state school graduates out-perform independent school graduates by four percentage points.

“We hope that this sets the record straight, and we’re sorry for any confusion.”

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