Raab, who is second favourite in the race to be the next prime minister, made the case for privately run state schools in 2013 and again in 2014, saying the government should open up the education system for companies to make money.

The idea is one of a number of rightwing proposals put forward by Raab in pamphlets over the years. The former Brexit secretary has also suggested encouraging more private companies into the NHS by giving them tax breaks or paying them premiums, and scrapping the 45% top rate of income tax, instead having a basic rate at 15% and a higher rate at 35%.

Asked whether Rabb still endorsed the idea of letting companies run state schools, his spokesman did not rule out the proposal, saying: “Dominic has set out his priorities to fight for a fairer Britain – a fairer deal for workers by cutting taxes for those on low and middle incomes, a fairer society by boosting apprenticeships and getting a fairer deal from Brussels.”

In his 2013 paper Capitalism for the Little Guy, Raab suggested the government should “lift the bar on profit-making companies running academies and free schools”, subject to a minimum of 50% of profits being reinvested into the school. At present academies and free schools cannot be run for profit.

Raab wrote that opening up schools to profit-making companies could help to raise capital investment for education at a time when funding from central government was under pressure, arguing that such a move would help raise standards.