Pupils from ten private and grammar schools are 100 times more likely to apply for the most prestigious graduate schemes than their peers who were educated at the bottom ten per cent of schools, regardless of which universities they went on to, new analysis has revealed.

Jobs at the most sought after law firms, management consultancies, banks and FTSE 100 companies - which offer starting salaries to graduates of around £45,000 - are dominated by applications from an elite set of schools.

According to research carried out by Rare, a recruitment company which specialises in encouraging diversity in the workplace, 30 per cent of sixth form students at the top ten schools had applied for the most prestigious graduate schemes.

This compares to just 0.3 per cent of students at the bottom ten per cent of schools, meaning students educated at the ten schools were 100 times more likely to apply than those at the worst.

These include Westminster School, which charges £36,000 a year for boarders, and whose alumni include former deputy Prime Minister Nick Clegg and the author A A Milne.