Collaborative research by the University of Cambridge, the University of Bristol and the Institute of Fiscal Studies has suggested that a lottery system of admissions could make the intake of Britain’s leading schools and universities fairer.

The research was based on the Millennium Cohort Study, which follows the lives of 19,000 children born in the United Kingdom in between 2000 and 2001.

The findings highlight how greater opportunities are afforded to children from families living in the catchment areas for the best quality schools. As houses closer to good quality schools are more expensive, there is a systematic bias towards families with a higher income.

The study comes amid on-going debate about elitism at Britain’s top universities. As low-income families are squeezed out of catchment areas, their children are left to poorer quality schools.

This is then reflected in the density of Oxbridge applicants from well-off areas with good schools. For example, in 2013 Surrey sent almost as many young people to study at Oxbridge as Wales and north-east England, with figures of 868 applicants and 1,187 respectively.

The researchers argue that existing plans to target elitism, such as priority admissions to low-income families, are only a source of help to the poorest 15 per cent of families.

They suggest a number of alternatives, including a lottery system, the reservation of places for applicants living outside the school’s catchment area, and a banding system that would take into account different abilities and backgrounds.

Lead researcher Professor Simon Burgess, of the University of Bristol’s Centre for Marketing and Public Organisation (CMPO), has said that there is an intended “nirvana” of excellence in all schools, but suggests that government officials “should not ignore the question of how places in the better-performing schools are allocated”.

However, Jack Smith, a second year undergraduate at King’s College, studying HSPS, described Burgess’ “nirvana” as a matter of “deflection, pure and simple”.

“With a lottery system they’d be treating a symptom rather than a cause,” he said.

“The fact that there’s such a gulf in quality between ‘popular schools’ and ‘everything else’ is the root of the problem.”