Blunkett gives selective reassurance only
But the head of historic Tiffin School - a boys' grammar in the London borough of Kingston upon Thames - did not pop champagne corks.
"Am I completely reassured by Mr Blunkett? No," says Dr Dempsey. "If Labour wins the next election I don't think grammar schools will go immediately, what happens two or three years down the line is more uncertain."
Dr Dempsey is disturbed by the prospect of parents being allowed to trigger a ballot on grammar schools. Before the Greenwich judgment of 1989, which ruled that education authorities cannot give priority to their own residents, he would have been confident.
Tiffin School picks 140 children from around 75 primaries each year, taking those with the highest results in two reasoning tests. Since 1989, only around half the pupils have come from Kingston. The rest travel from Merton and Surrey.
"If Kingston parents had more access to our school I think we would have a lot of support. But some parents are disappointed that so many children come in from outside the borough," he says.
He is comforted by the belief that Mr Blunkett "genuinely cares about each child's education in the classroom". He would be "devastated" if the school - where each year around 55 per cent of pupils gain A and B grades at A-level and 90 per cent go on to university - were to be reorganised.
"We have a very distinctive ethos." This would be lost if Tiffin was no longer a grammar school.
"There would be a great deal of disappointment, a lot of staff would leave and all the children at the school, as well as those coming in for at least six or seven years, would suffer."
The national debate on selective education is echoed at local level. Jeremy Thorn, leader of the Kingston Labour group and Labour education spokesperson, wishes there were no 11-plus. But he says he is not interested in "destroying good schools".
"We would not want to make changes to the school system without a democratic mandate," he says. "The quality of our non-selective schools is so high and the two grammar schools are so difficult to get in to that fewer and fewer Kingston children apply. Only 10 per cent or less of Kingston children now go to the selective schools. My hope is that ultimately they will wither on the vine. "
John Heamon, chair of education and leisure in the Liberal Democrat-controlled borough, says Mr Blunkett's line is almost identical to his own party's. "We don't favour an expansion of selection, but we believe schools have been through an enormous amount of unheaval and we are going for a period of stability.
"Ultimately, the future of existing grammar schools should be a community decision," he says.
But Dennis Doe, education spokesman for the Conservative group, says Mr Blunkett is not to be trusted. "His words may sound reassuring, but the real heart of the Labour party is anti-selection, pro-mixed ability. When it comes to the crunch, the rank and file will make the decisions and they will try and get rid of our grammars," he says.
Whether old Labour would succeed, however, is another matter. According to Janet Irwin, head of King Athelstan Primary School, Kingston, many parents move to the borough for a grammar education for their children.
"If they're going to go for parental consultation, Kingston's grammar schools will remain," she says. "Some parents opt not to put their children in for the test, but it's often because they don't think they will pass rather than because they don't like the system."
Catherine Mumford, who has three children at King Athelstan, wants grammars abolished. She resents the fact that so many grammar pupils come from outside the borough.
She says competition is so high that a child whose parents cannot afford to pay for a private tutor has virtually no chance of passing the exam.
"I don't trust David Blunkett. One minute he says one thing, the next it's something completely different. It's all a ploy to keep his party in favour for the election."