Mr Denham called on Labour to confront a "difficult truth"
The political left must stop "holding up egalitarianism as the ideal", Communities Secretary John Denham has told the Fabian Society think tank.
Basing fairness purely on "society's response to those in greatest need" risked being unpopular, he said.
He called for a "different, more nuanced view of fairness and equality".
His comments come as an Equality Bill is going through Parliament which would make public bodies consider social class gaps when forming policies.
Mr Denham said that the numbers within society who signed up to the traditional egalitarian view were "simply too small to construct a strong, viable and inclusive electoral coalition".
He told the Fabian Society: "We must confront the difficult truth: that this form of egalitarianism, the one that defines fairness solely in terms of society's response to those in greatest need, is badly out of step with popular sentiment.
"A rejection of inequality - both absolute, relative and of opportunity - is absolutely core to who we are. But we will be more successful - not just electorally but in challenging unacceptable inequality - if we adopt and own a different, more nuanced view of fairness and equality."
Mr Denham said Labour had to relate to the aspirations of people on middle incomes, adding that this group felt excluded by policies and language aimed at 'the poor'.
He said this group were in fact more concerned about those in higher social classes.