A Freedom of Information request by student body NUS Scotland found St Andrews University – where Prince William studied – recruited only 13 students from the most deprived backgrounds of the country in 2010/11 – 2.7% of the student intake.
The second lowest proportion was at Aberdeen University, with 51 students from the most deprived backgrounds, amounting to 3.1% of its student population.
Edinburgh University had just 5% of its student population entering in 2010/11 from the most deprived sector relative to the Scottish Index of Multiple Deprivation (SIMD) – a total of 91 students.
The SIMD measures people against current income, employment, health, education, skills and training, geographic access to services, housing and crime. Glasgow, Edinburgh, North and South Lanarkshire and Dundee have the worst concentrations of deprivation.
Robin Parker, president of NUS Scotland, said: "These statistics are shocking. For an institution like St Andrews to take 13 students from the poorest backgrounds last year shows just how badly some of our institutions perform.
"University places should be given to those who have the most talent and potential. Unless institutions do more to widen access, they're missing out on some of those with the most potential who could get the best degrees. They are, quite frankly, not doing their job properly."
However, Alastair Sim, director of Universities Scotland, which represents university principals, said the data should not be interpreted as a lack of commitment among universities to widen access.
"To deliver significant change in universities, you first need to tackle the root of the problem, which is the large gap in attainment according to deprivation in schools, as recent reports have confirmed," he said.
"We are working to open up opportunities – such as articulation, admissions taking account of context, summer schools and close engagement with primary and secondary schools – and will be looking at what more can be done."
The latest figures come just a few weeks after The Herald revealed that Scottish universities are recruiting a smaller proportion of students from working-class backgrounds than 10 years ago.
The situation has arisen because access to university is tightly controlled, with pupils given priority depending on their exam results.
Because poverty has a direct impact on academic achievement, pupils who are bright enough to go to university can fail to achieve the qualifications that allow them to do so. To counter this, universities have developed schemes to attract those from poorer backgrounds – with some institutions offering lower entry grades to those who complete access courses.
Universities have also been asked to accept students into the second or third year of degree courses after they complete Higher National qualifications at colleges – so-called articulation.
More recently, the Scottish Government announced plans to give universities binding targets on widening participation, with the prospect of fines for those that fail.
However, universities have opposed the move, arguing the problem is largely not of their own making because of the markedly differing attainment between pupils from deprived and middle-class areas that can develop in primary school.
John Field, Professor of Lifelong Learning at Stirling University, called for greater use of articulation.
He said: "We have always had a special card to play in Scotland to help with this and that is articulation of Higher National qualifications where students can move from college to university.
"There is plenty of evidence that universities are simply not taking articulation seriously."
A spokesman for the Scottish Government added: "We have seen an increase in participation rates in higher education in recent years, including a narrowing of the gap between the proportion of students from the most and least deprived areas.
"However, we are determined to do better, which is why we will be introducing statutory widening-access agreements."
The statistics, which relate to the most deprived 20% of the population, are taken from NUS Scotland's forthcoming report on widening access in Scotland.