Since 1997, there has been a 49 per cent rise in undergraduates selected for the country's leading 13 institutions from areas that traditionally send very few students to university.
Student numbers from "low participation" neighbourhoods grew faster than those from wealthier areas, which rose by 20 per cent.
Birmingham university recorded an 87 per cent increase in students from poorer areas, from 265 in 1997 to 495 in 2002, while the figures for Bristol and Durham were 68 and 67 per cent respectively. At St Andrews, they were only 8 per cent.
The other universities were Cambridge, Edinburgh, Imperial college, London, the London School of Economics, Nottingham, Oxford, University college, London, Warwick and York.
The trust, which funds educational projects for youngsters from non-privileged backgrounds, said the increases had been achieved without the universities lowering academic standards.
Average A-level point scores of students admitted to the 13 institutions increased slightly over the period.
Sir Peter Lampl, the charity's chairman, said the figures undermined claims that the Government's drive to increase the numbers studying at university was not widening access.
He said the welcome turnaround suggested "a much-needed levelling of the playing-field as far as university admissions are concerned".
"But the numbers are still small. Despite accounting for 30 per cent of young people nationally, students from low-participation areas make up only 8 per cent of entrants to the top universities.
"Based on their A-level performance, there should be more of them."