The research by the Sutton Trust suggests that admissions ballots are not as unpopular as commonly supposed.
When Brighton and Hove council adopted balloting earlier this year, the moves were attacked as social engineering and for reducing education to a "game of chance". But supporters believe it is fairer to poorer parents who cannot afford houses in expensive catchment areas.
Several other councils are known to be considering the system, and it was given additional backing this week by Sir Cyril Taylor, chairman of the Specialist Schools and Academies Trust, who told MPs he supported it.
The Sutton Trust poll found 36 per cent of parents thought ballots were the best way of allocating places to oversubscribed faith schools. Nearly a third believed it was the best system of deciding who should win places at popular comprehensives. Allocating places depending on religious background, the system for the most oversubscribed of England's 7,000 faith schools, was the least popular method.
However, when asked in general what was the fairest approach, only 9 per cent of parents opted for school lotteries.
Sir Peter Lampl, chair of the Sutton Trust, said the results suggested parents were more favourable to lotteries when they were given the options in context.
"If you give parents a specific situation, they can often see it's fairer than deciding on the basis of whether you live 10 yards nearer the school or whether you've got a letter from the priest," he said.
He complained that the debate had been hijacked by the "Mercedes Benz set"
who sought to manipulate the schools admission system to their own advantage.
Margaret Morrissey, spokeswoman for the National Confede-ration of Parent Teacher Associ-ations, said she was surprised by the result.
"Parents feel ballots devalue the system of education," she said "It's a choice you should be able to make in advance, not by drawing lots at the last minute."