University performance data published by the higher education funding councils reveals that only 59% of undergraduates entering St Andrews come from state schools.
A university of its type is expected to admit over three-quarters from the state sector.
The University of St Andrews received a popularity boost when it was chosen by Prince William.
However university league tables suggest it is not taking as many students from state schools as it should.
Table of state school participation
Table of drop-out rates
St Andrews does not have the lowest overall figure - Oxford takes only 51% from state schools - but St Andrews has the worst record when compared with universities with similar courses and admissions requirements.
Drop-out rates
The league tables compare admissions from state schools against benchmarks set for each university.
St Andrews appears to do worst, falling 18 percentage points below its target. University College London fares only slightly better.
"
You cannot change the social makeup of a university over night
"
Dr Brian Lang, Principal at St Andrews
Oxford and Bristol come next, falling 16 percentage points below their expected figure.
The university tables also show student drop-out rates. The highest appears to be at the University of North London where 41% fail to complete their degree.
Others with a poor record are Thames Valley University and the University of Paisley.
All three take a high proportion of mature students which may explain the higher drop-out rates.
Slow progress
The Principal of St Andrews, Dr Brian Lang, said the university was trying to reach out to a more diverse range of students through initiatives with state schools.
But he warned: "It's going to be a long haul."
"You cannot change the social makeup of a university over night - it won't take a year, it won't take two years. it'll take longer than that," said Dr Lang.
"The fact is we're taking steps to redress our population balance and in the long term those steps will pay off."
President of the Students' Association at the university, Dana Green said she did not think St Andrews had a problem with elitism.
"I don't find it a posh university. I've been here a while now and I find it's quite a good mix of students," said Ms Green.
"We could always improve and certainly most universities in Britain are trying to improve their diversity of students."
Indeed, Sally Hunt, assistant general secretary of the Association of University Teachers, said the figures did not reflect the hard work undertaken by university staff to help widen access.
"Universities are already creaking at the seems and there will not be any meaningful expansion of access to under represented groups without further investment," she said.