Barnaby Lenon, who also chairs the London Academy of Excellence, a selective state sixth form supported by leading private schools, told TES that selective schools with large numbers of Cambridge applicants would quickly become good at preparing them for the tests, which were announced last month and will be sat for the first time next year.

“[Indpendent schools] will have many more students apply to Cambridge, therefore will build up experience of the Cambridge tests more rapidly,” he said. “There’s a difference between a school that has 50 or 60 applicants a year and a school that may have two or three.”

The university says the new assessments “aren’t pass/fail tests” and students’ performance will be considered alongside other parts of their application, such as an interview and a piece of written work. It says the assessments, which will be specific to the course a student applies for, aim to help the university to get a better understanding of candidates’ comprehension skills and thinking skills.

Mr Lenon, who was head master of Harrow school until 2011, acknowledged that the tests would be just one factor among many in the admissions process, but urged state schools to start tutoring their brightest pupils in preparation for them - despite the university’s insistence that no tutoring is required.

“The most important thing is for schools to realise that it is important for students to prepare for these tests,” he said. “It’s difficult for schools to fit in time for tutoring, but they should do it…I believe all tests can be prepared for, to some degree.”

Mr Lenon added that schools should spend about an hour per week preparing students for the tests. They should do this “for as many months as they can, ideally starting in year 12,” he added.

He said he “completely understood” why the university had introduced the new assessments. “The exams system makes it hard for them [the university] to discriminate at the age of 17,” he said.

But a spokesman for the university said: ““We have the expertise needed to devise assessments which are appropriate for academically gifted Year 13 students from all backgrounds.

“No advance preparation will be needed, other than revision of material already being studied at school, and only where indicated for specific courses.”

He said the university would “ensure that all of the information that applicants need is freely available online” and would provide teachers with a guide to the assessments.