The Mori poll, carried out for the Sutton Trust, an education charity, found that just 36 per cent of parents were opposed to selection by ability at the age of 11 or 12.
The trust wants top private schools to be opened up to all, regardless of their ability to pay. But the poll showed affluent families were much less enthusiastic about the idea than their working-class counterparts.
While 47 per cent of the 644 parents polled said the Government should pay towards private-school places, 46 per cent from social classes A and B disagreed.
By contrast, only 18 per cent of parents from classes D and E were opposed to the idea.
Overall, 22 per cent said they would go private if money was not an issue, while 28 per cent said they probably would.
The trust wants the Government to expand a pilot open-access scheme it is funding in Liverpool.
The Belvedere school, a private Merseyside girls' school, is open to any girl who meets its entrance criteria. Seven out of 10 families of pupils receive financial help with the pound;2,159 termly fees, at a cost of pound;2 million a year.
Expanding the scheme to cover 100 academically excellent private schools would eventually cost the taxpayer pound;200m a year, the trust said.
Sir Peter Lampl, the trust's chairman, said: "Opening up 100 per cent of the places at our top independent schools, on the basis of merit and regardless of income, would change the nature of those schools and lead to the removal of the unparalleled educational apartheid which exists in this country."
The charity urged the Government to start breaking down such "educational apartheid" by introducing open access to 12 private schools.