Earlier this year, Ms May took on private schools when she accused them of being “divorced from normal life” as she warned them they needed to be more proactive in looking after the interests of pupils from disadvantaged backgrounds.

Speaking ahead of the Independent Schools Show, which takes place this weekend, Prof Bailey he told the Evening Standard her plans should be “proportionate”.

He said: “I am not convinced that those comments were based upon a detailed knowledge of what independent schools do.

“There is a mass of information out there about the extent of the wider contribution they make to society and that should be properly evaluated and weighed.