Labour's draft manifesto, to be published today, will reveal the dream as a paramount aim of Government, to be offered without strings or catches.
It states: "We want to raise a family with decent pay and prospects; a home that is affordable and secure; schools of quality for our children; to be able to walk on the street at night without fear; to know that if we are ill we will be treated on the basis of need, not wealth; and we want security and dignity when we grow old ... These are the fundamentals that matter to the people of Britain." But the document adds: "These aspirations, the basis of the British dream that our children can do better than us, are under threat."
Promising direct action to help deliver the dream, Mr Blair will say that Labour will cut class sizes in schools, reduce hospital waiting lists, switch 250,000 unemployed youngsters from benefit to work, counter youth crime, and maintain low interest rates by determined action on inflation, public spending and borrowing.
The document recognises that it is more than 20 years since Labour was last elected to Government, and concedes that the Tories will play on people's fear of the unknown.
But it assures voters that it offers only clear, practical promises that a Labour Government can deliver - as opposed to "promising the world, and delivering nothing ... "The same process of change we have brought to our party, we will bring to the country."
The pledge to deliver the "British dream" is a return by Mr Blair to a theme he used during the 1994 leadership election. It inspired party members then, and he clearly hopes it will inspire voters.
But the document goes to great lengths to define New Labour, and its new position in the political spectrum.
"Labour is neither old Left nor New Right," it says. "We offer a new way that leads from the centre but is profoundly radical in the changes it promises."
According to the document, voters are asking : "What can we expect from a Labour Government? How will life be better for me and my family?" In sections covering the economy, education, welfare, health, law and order, the environment, transport, security and international relations, it seeks to provide replies.
"The answer is not to go back," it says. "There were great achievements of previous Labour Governments - not least the National Health Service. But we have changed the Labour Party because it needed to change."
Nevertheless, voters should vote Labour "because it is based on the fundamental principle that the individual does best within a strong and unified society where we acknowledge that success depends not just on the striving of the individual, but on working together.
"It is new because it seeks to apply that principle entirely afresh to a different and changing world."
Mr Blair will say that Labour can deliver its five specific promises without tax increases, on the basis of a manifesto that has been costed throughout.
However, a leadership source said last night that the party was still saying nothing either way about the possibility of introducing a higher- rate income tax band for the well-off.
Some Labour frontbenchers believe that any such move would now be counter- productive, and might cause more electoral damage than it was worth in terms of the cash that might be raised.
In an interview with today's Daily Mirror, Mr Blair says he wants a new trust on tax with the British people, adding: "None of our proposals involves raising people's taxes ...
"I want people to understand that a Labour Party that represents ordinary people in this country is not getting into power so that it can bung their taxes up."
Asked if he has behaved like a dictator in drawing up the manifesto document, he said: "I don't accept that. I have been firm in giving leadership to the Labour Party because that is what the situation requires."
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