A philanthropist is looking for state schools to accept his offer of scholarships for poor white boys after two leading private institutions said that taking the money would be against their values.

Professor Sir Bryan Thwaites said he was “surveying the field” of first-class state academies that would be “only too glad to accept money” on his terms.

He had approached Winchester and Dulwich colleges, which dismissed his offer. The schools are among the most expensive in England, charging maximum fees of about £40,000 a year.

Both are trying to broaden their intake by offering financial support to those unable to afford the fees. Dulwich has an ambition for half its pupils to be on scholarships or bursaries. Neither wants to put ethnic restrictions