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Lord Hattersley told BBC Radio 4's Today programme that the government's Social Exclusion Unit, established in the Cabinet Office last year, had done nothing to help the poor.
It was "leaving people in poverty in the way a Labour government has never left people in poverty before," he said.
Lord Hattersley said: "This is the first Labour government to come to power in decent economic circumstances.
"It is also a first Labour government to come into power which has not increased the basic rates of benefit, which has not increased the basic pension and the supplementary pension.
"Whilst the unit has been working the pensioners are dying and people have been getting further and further down the breadline.
"That is the sort of direction that has to be changed and I don't think Peter Mandelson going is going to make very much difference."
Lord Hattersley, who was an MP until the last general election, made his remarks during an interview about former trade secretary Peter Mandelson's resignation.
Mr Mandelson's abrupt resignation over a secret loan from ministerial colleague Geoffrey Robinson, who also resigned, would make no difference while basic rates of pensions and benefits remained unchanged, he said.
The former trade secretary had taken a leading role in the unit's formation in his previous role as minister without portfolio.
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