They are planning to break away from the local authority selection system and introduce their own tests from next year.

The proposals from Rainham Mark, Rochester Girls’ and Chatham Girls’ schools in the Medway in the north of the county have been widely condemned by local authority heads - and found little support from nearby GM schools.

Criticism centres on the proposed timing and venues of new tests and their format, amid claims that the schools want to become super-grammars and cream off pupils.

There are also doubts about the “common currency” of selection in Kent and that parents might be confused by the array of tests operating in the county.

The three rebels want to carry out their own tests on a Saturday morning in their schools during the first term of pupils’ final year at primary school.

And Mrs Ingeborg Watson, head of Chatham Girls, which is currently consulting on the proposal, said: “We would try to co-operate with the local education authority on admissions.”

She said the schools wanted to use a national test - possibly one offered by the National Foundation for Educational Research - and to reintroduce verbal reasoning.

Under their proposals, pupils would sit a test in the autumn term - six weeks before the local authority run tests.

Mrs Watson said the current selection system in Kent was complex, and said: “We are not saying the Kent system is wrong, or our system is better. At the moment it is very difficult to marry the two. We just want to introduce our own system to simplify matters.”

She did not believe that the timing of the proposed tests would make a great deal of difference.

But the head of a local primary, who did not want to be named, said: “Tests in the autumn term will challenge some children who are just not ready to take selection tests at that time.

“It also means that if children know where they are going before Christmas we are going to have a hell of a job working with them because they will be ready to go.”

So far, only Rochester Girls has published the public notice on its proposals for change. Chatham Girls and Rainham Mark are still consulting.

There are six grammar schools in north Kent. Three grant-maintained (two girls and one co-ed) and three run by the local authority (one girls and two boys). Competition for pupils - and the money they bring with them - is fairly fierce.

Keith Williams, head of Sir Joseph Williamson’s Mathematical School, an LEA grammar, said the main objection was to testing pupils not too long out of Year 5.

A meeting of more than 50 primary headteachers unanimously condemned the proposals.

And Mr Williams said: “We are left wondering what educational justification there is for earlier testing. The impression we get is that it is more designed to suit the needs of the grant-maintained grammar schools in that they would know their numbers earlier than the needs of the children. These proposals are not helping relations between the local authority schools and GM schools although we are still speaking to each other.”

Mike Newbold, head of Oakwood Park, a GM grammar in Maidstone, has declined to go along with the proposal, which will require the Secretary of State’s approval. He said: “There is a great danger that the admission procedure is going to fragment so that parents and children are going to traipse from school to school doing all sorts of tests. The more literate parents might have an idea what to do, but less intelligent parents might not be able to follow complex procedures.”

He said he was also worried that the “common currency” of selection in Kent would be dissipated. “I could run my own tests and I would know what they meant, but they wouldn’t equate with ability in other parts of Kent.”