And, in a speech that may further alarm the Labour left over his plans for the welfare state, the party leader underlined that Labour was "not about bigger benefits" but about "moving people from benefit to work".
Both parties, he said in a speech to the annual Newspaper Press Fund lunch, were "in a state of transition. As the critical mass in the Tory party moves further and further to the right, it is Labour that is increasingly the party of the centre and the left of centre". In a divided two-nation Conservative Britain, Labour was now the party of one-nation politics. That mantle "no longer fits the Tories. It is draped rightly around our shoulders".
For tackling the issue of inequality and a growing underclass was now a "middle-class" and a majority mainstream issue, "not just an issue of compassion but of economic efficiency".
Unemployment wasted talent and denied the country the wealth-creating abilities of the jobless while pushing up taxes and spending to meet unemployment itself, crime, welfare and social decay. Resulting tears in the social fabric created "alienation amongst one group and insecurity and concern amongst the rest. Even the better off cannot escape its consequences".
The means of tackling it should be "through the politics of opportunity, not the politics of envy. It is about levelling up, not levelling down, extending opportunity to those denied it, not taking it away from those that have it." Labour wanted social justice "not out of well-meaning sympathy for the poor ... but because we know an unfair society is an ineffective society".
But his speech contained a warning that the solutions would be "definitely new Labour", equipping people to cope with the global and technological changes now happening, not resisting the change.
"That is why Labour is not about bigger benefits but moving people from benefit to work." It was why Labour "must champion excellence and achievement in all our schools. Why we must combine choice in society with a strong sense of responsibility to it, not least in the area of crime. Why we must move beyond the sterile battle between public and private sector to a sensible modern partnership between the two."
The speech reflects the determination of Mr Blair and of Gordon Brown, the shadow Chancellor, to shed for good Labour's image as a high-tax party dedicated to penal redistribution, while insisting Labour will still tackle inequality.
Britain was witnessing an underclass at the bottom and greed at the top, wrecking social cohesion, Mr Blair said. And while hundreds of millions went to those at the top of the privatised utilities, jobs were being shed and pay was just keeping pace with inflation for the rest.