In the survey of 2,500 adults, 33 per cent agreed and 26 per cent strongly agreed with the statement: "In order to retain their charitable status, independent schools should do more to demonstrate the way in which they benefit the public". Only 11 per cent disagreed.
The findings come in advance of the Charity Commission's delayed publication of its guidance on public benefit. The document is now due to be released next month.
Thirty-six per cent of respondents - only 9 per cent of whom had ever sent children to independent schools - thought that offering assisted places to children from low income families was the best way to demonstrate public benefit, while 19 per cent advocated offering facilities for community use.
Eight per cent thought sharing staff with the state sector would be the best way, while 13 per cent opted for "providing a higher standard of education than state schools".
Tom Shewry is head of education at Zurich, which insures many schools. He said the financial impact on schools would depend on the requirements in the Charity Commission's forthcoming guidelines.
"A few independent schools have started the process of transferring back into the state sector to become academies," he said. "However, until a greater understanding is gained, it shouldn't be seen as an automatic option."