One candidate who was on track to receive 10 highers, having already obtained six As in fifth year, was rejected for the LLB course because there was no space left.

The pupil’s mother, who lives in Lanarkshire, said that while she supports the ‘levelling-up’ agenda, she had been taken aback “by the lack of balance and fairness in the system as it appears this year”.

Scotland utilises a five-point postcode-based poverty scale, known as the Scottish index of multiple deprivation (SIMD), which Shirley-Anne Somerville, the education secretary, has admitted is flawed.

Allan Crosbie, executive member of the Educational Institute of Scotland (EIS), the country’s largest teaching union, said the Scottish index overlooked “hidden poverty in rich areas” while also labelling rich students as deprived.

“Rich families are living in SIMD1-2 [deprived] areas. There might be children of an MP living in these areas,” he said.

In a letter seen by The Times, an official at the university said: “The large rise in application numbers seen this year, coupled with the rise in the number of students achieving top grades in 2021, means that we have seen a further increase in competition for places. Unfortunately, this has meant that we haven’t been able to offer to all applicants who have achieved even the very highest grades … and we give priority in selection to widening access applicants.”

An Edinburgh University spokesman said: “The university takes its commitment to widening access very seriously and recognises that a long-term and sustained effort is required to achieve meaningful social mobility in communities.

“Our contextualised admissions process allows us to make offers to widening participation applicants who meet the minimum academic requirements, while taking into account a range of factors other than academic qualifications. The university has used contextualised offer-making since 2004 so this is not a new way to identify and recognise potential to succeed. The minimum entry requirement for our Law LLB programme for applicants in Scotland is ABBB, and most widening access applicants have grades well above this minimum.

“The outcome reflects the very high attainment of applicants this year, our efforts to widen participation for those studying law, and the limited number of places available on the programme. The number of students we can accept from Scotland is capped by the Scottish government, which means that applicants are only in competition with those who are also within their own fee pool i.e. Scotland, Rest of UK and international.”