Some 64% of privately educated A-level students got into the most selective universities in 2010-11, against 24% of state school pupils.
But the chances of the very poorest pupils have improved according to official figures.
The government said record numbers of disadvantaged 18-year-olds had applied to university this year.
The Department for Business Innovation and Skills (BIS) data is published a week before this year’s A-level results for almost 300,000 students.
Despite efforts by universities and the government to broaden access to university the statistics suggest privately educated students are not only more likely to go to university but are more likely to get places at institutions requiring better A-level results.
The figures also suggest the chances of the poorest pupils are improving although they still lag behind their peers from better-off families.
In 2005-06 only 13% of pupils on free school meals made it to university. By 2010-11 this had improved to 20%, but the figure for pupils