The proportion of independent school parents in the top social group, class A, is up 8 per cent compared with five years ago.
The percentage from every other social class is down apart from that for those at the bottom of the heap, which remains unchanged at 1 per cent.
Figures in a MORI poll commissioned by the Independent Schools Information Service (Isis) show that the proportion of private school parents from the top social class has doubled in a decade. Two similar polls were carried out in 1989 and 1993.
Last year, 30 per cent of parents were in class A compared with 15 per cent in 1989. Thirty nine per cent were in class B and just over one-fifth were in social class C1.
A spokesman for Isis warned that the Government's decision to abolish the assisted places scheme which subsidises bright pupils from poor backgrounds in independent schools would make the position worse.
"On the face of it, it does look as though independent schools are becoming more socially exclusive. It is something we have been anxious about for some years. In the 1993 survey, we assumed that it was the result of the recession. It may well be that that effect is still with us."
Nearly two-thirds of parents with children at independent schools have incomes of more than pounds 40,000 a year.
In just over half the families questioned, the parents were first-time buyers and neither of them had attended a private school, a slight decrease on the figure in the previous poll.
For the survey, questionnaires were sent to 1,550 parents from 62 independent schools and 737 replied.
One in four of the respondents said that the decision to choose a private school was influenced by the fact that they had smaller class sizes, up from 18 per cent in 1993.
The proportion choosing an independent school because they were dissatisfied with state schools was up slightly, from 20 per cent to 22 per cent.
Six out of ten parents said that their children's opinion had influenced their choice.
Very few - just 16 per cent - said that they were concerned about a school's position in newspaper examination league tables, although 63 per cent rated exam results as important.
Boarding schools are still hampered by an image problem, the report says. "While they are thought to be good for character building," it says. "They are deemed weak academically and the preserve of the rich."