Heads of existing grammar schools view Labour's plans to allow local ballots on the future of selective education as unworkable.
Labour is insisting that decisions on the abolition of any of the remaining 150 grammar schools will be based on the outcome of a ballot of parents with children in feeder primary schools.
However, heads such as Malcolm Cavendish of Handsworth grammar school for boys believe Labour's policy will prove impractical to implement. The more prestigious schools may even opt to become independent, he says.
According to Labour education spokesman David Blunkett's office, ballots would only take place where there is evidence of local demand for a vote on the issue. The evidence could be a petition from parents with children in local primary schools.
Critics of the policy point out Labour will have problems defining which parents are eligible to vote and will have difficulty drafting a ballot paper.
Neil Slater, head of Dover boys' grammar school, says: "Are they talking about balloting all parents in Kent or only those parents who live near the school? To some extent, the choice of electorate will determine the result."
At the neighbouring girls' grammar school, head Elizabeth Lew, opposes the principle of parental ballots on the grounds that they will lead to greater social division.
"In west Kent, middle-class parents in Tunbridge Wells are more likely to get grammar school places because 33 per cent of pupils are in selective schools.
Here in south Kent, where the local community is predominantly working-class, there are places for 22 per cent of the population. Parents in this area are therefore more likely to vote for an end to selection," she says.
The result could also hinge on whether Labour opted to ballot all parents with children in primary schools or only the parents of older children about to transfer to secondary.
Should Labour win the election, the first test of its grammar school policy is likely to be in Trafford. The local Conservatives, who until the last local elections had controlled the council for more than 20 years, have always attributed their success to a low council tax and the popularity of its grammar schools.
The new ruling Labour-Liberal Democrat group wants to introduce a non-selective system, but it is unlikely to proceed until there is a sympathetic government.
Interviewed by Jonathan Dimbleby last Sunday, Mr Blunkett was clearly irritated by the focus on the party's policy towards grammar schools.
Labour, he says, is about levelling up standards in schools and grammar schools are not central to the party's education policy.
He rejects the charge that parental ballots on grammar schools are impractical. They will be held, he says, in those areas where there is demand from parents.
A future Labour government would consult on the " mechanistic details".
The problem for Labour is that until there is more information on the "mechanistic details", its critics will point to the problems.