Mr Phillips said people were "very keen" for change
The Equality and Human Rights Commission must be given the power to fight the class divide in Britain, its chairman has said.
Trevor Phillips told BBC Radio 4's World at One he would launch a "new assault" on inequality and wanted an extension to the organisation's remit.
The economic slowdown meant people were "very keen" for change.
Everyone was "happy to take some of the pain as long as that pain is shared fairly", Mr Phillips added.
A report by the commission says there is too much "vertical" division in Britain between social classes.
It states: "We are not just limiting our description [of inequality] by gender or race but we are also looking at this extremely important issue of class."
Mr Phillips said: "We have to tackle the causes that drive inequality in our society and I think, to be honest, the public is very, very keen on this at the present time.
"People can see the economic slowdown coming. Everyone is happy to take some of the pain as long as that pain is shared fairly and what we want to do is to make sure that the burden doesn't fall unfairly on some groups rather than others."
BBC home affairs editor Mark Easton said this was "a radical departure which is likely to be criticised by some as an implicitly political policy from a statutory body that must remain independent of party ideology".
It would "mean taking on the wealthy and educated middle class who are adept at playing the system to the advantage of their families", he added.
The commission was established in 2007, replacing the Equal Opportunities Commission.