John Wotherspoon, headteacher at Willesden high school in north-west London, believes most of his parents would "probably be offended by the term middle class". But only by attracting those kinds of families can the school become "truly" comprehensive, he said.
"Many of our families have to cope with living in hostels and having no financial security.
"Every parent wants their child to do well - but that means different things to different people. An unemployed parent might aspire to their child getting a job whereas a middle-class family might want them to become a solicitor or doctor." said Mr Wotherspoon.
"Tony Blair's ideas are all in his own mind. Here families are facing problems that are outside class. Being middle class isn't even something they could even begin to aspire to," said headteacher Phillip Farnham of Beauherne county primary school in Canterbury
"Middle-class families do live on the doorstep of the school, but they drive their children to school elsewhere. The school serves a council estate where parents are more concerned about protecting their children from poverty and unemployment than worrying about ideas of class.
"Most of our parents would probably say they were working class because their parents were. But most are unemployed and have very little stability in their home life," Mr Farnham said.
"Getting middle-class children into the school would immediately give us a better balance of academic ability and encourage other parents to consider us."
Marion Parsons, headteacher of Islington Green school in north London, agrees. Her school was one of those rejected by the Blairs for their two sons when they lived nearby before Labour's 1997 election victory.
"From where I'm standing it is patently not true," said Ms Parsons. "Some of the children here are impoverished in every conceivable way.
"If some of the values we associate with being middle class are respect for others, deferred gratification, hard work and a belief in education - I can't say that from where I am that that's true."
Moreton Community School in Wolverhampton used to be a "genuinely working-class school". It still would be, if only its parents could find work, said headteacher Rod Sheppard.
Many have been in and out of jobs since the town's engineering industry collapsed in the 1970s.
"We have no middle-class families here. If we had an influx of middle-class aspirational parents it would have an immediate impact on the whole school," said Mr Sheppard.
"It would raise the school's profile and some of those aspirations might rub off on the other children. We try to get children to realise that education is the key to having a brighter future than their parents and older brothers and sisters. But it is a struggle."
Rick Widdowson, headteacher at Garston CE primary school in Liverpool, also questioned Mr Blair's analysis.
But he admitted: "I think there's been a shift. There's a kind of non-working class now of unemployed people. We have children from a fairly poor background, all the way through to the kind of families Tony Blair seemed to be referring to."
But is it even appropriate to talk of class in today's society? asks Joyce Ambrose, headteacher of Roundthorn primary school in Oldham.
"Two-thirds of our children are from ethnic-minority backgrounds," said Mrs Ambrose. "They don't really fit into class categories. That's probably a bit out of date in today's multicultural ethnic society."