Potential Cambridge undergraduates who fail to get top marks at A-level could be given a second chance by enrolling on a special one-year “foundation degree”, under radical new proposals.

The university’s new thinking on admissions came as Cambridge unveiled figures showing successful state school applications had risen to their highest point in more than a quarter of a century – but were still far below their 1980 peak. The proportion of new UK-based undergraduates from state schools will be 59 per cent this year – up from 55 per cent last year, but far below 69 per cent in 1980.