In a speech flagged as a vital ingredient in the development of Labour policy for government, Mr Blair told the Commonwealth Press Union in Cape Town: "It is upon the values of the extended family that the decent society will be built.
"Most children who are bad are made bad, not born bad," he said. "And we, their parents and the society we create, are what make them. It is in the family that we learn the difference between right and wrong."
Labour leadership sources said last night that Mr Blair was keen to move on from the party conferences with a positive agenda. But the Tories denounced him as "phoney Tony, the TV evangelist", who was attempting to take the moral high-ground while, in fact, using that as cover for an extension of state power and the creation of the "nanny state".
Mr Blair said nothing angered him more than the "nanny state" accusation. "Without support for family life, and for the norms of proper conduct towards one another, we all will suffer," he said.
He was also careful to offer a pre-emptive defence against those who might be tempted to accuse him of wanting to return to John Major's "back to basics" campaign.
"I have no desire," he said, "to return to the age of Victorian hypocrisy about sex, to women's place being only in the kitchen, to homophobia, or to preaching to people about their private lives as the ill-fated 'Back to Basics' campaign of the Conservatives attempted to do.
"But the absence of prejudice should not mean the absence of rules, of order, of stability.
"Let us construct them for today. Let the social morality be based on reason, not bigotry. But let us not delude ourselves that we can build a society fit for our children to grow up in, without making a moral judgement about the nature of that society."
Mr Blair said Labour's programme for child-care and for more nursery education would be good for children and for parents who wanted to work.
But parents had duties, too: duties to help schools, and to know where their children were, and what they were doing, after school.
"Dealing with truancy must be a combined effort of school, police, local organisations - and parents," Mr Blair said. "I get sick and tired of seeing parents say it's all the school's fault, the teacher's fault, society's fault, when often it may be their fault but they will not face their responsibilities."
He also said: "I can see no reason at all for young children to be out on their own late at night, and I can see many reasons why they shouldn't be - not least for their own safety. We are examining measures to tackle this. Some have called it curfew. I call it child protection."
Those two measures - on truancy and a curfew for children who had not committed a criminal offence - prompted a Conservative charge that Mr Blair wanted to use local "bureaucracy" to meddle in private lives.
While the Conservatives did not link the speech with their class-based attack on Mr Blair, the Labour leader volunteered: "Conventional wisdom has it that in the pursuit of middle-class support, we have alienated our traditional support among the so-called blue-collar workers. This is utter nonsense."
Because of the breach of Tory tax pledges, Labour had made "considerable progress' in winning middle-class trust, Mr Blair said. But the party was also gaining disproportionate support from the working classes, because of its tough approach to law and order.
"It shows how little many of our opinion-formers know of the world in which most people have to live that they assume a tough stance on law and order and support for family life calculated to appeal to the more affluent in our society ...
"While no crime can be excused, and while the costs of crime must be paid by all of us, it is the poor and disadvantaged whose quality of life has suffered most."
Mr Blair lamented the loss of "decent British values" but he did not believe that it was impossible to rediscover the best of those values.
"We need a new social morality for today that doesn't seek to recreate the past, but doesn't ignore the truth about our society just because it is convenient to do so," he said.
"The right claim to have won the intellectual arguments through the 1980s. But their laissez-faire policies have destroyed the very thing they claimed they would create: individual security and fulfilment."
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