David Davis has outlined his plans for referendums on returning powers he says have been lost to the European Union.
Mr Davis has made clear his Eurosceptic leanings
Mr Davis, who says he is not talking about quitting the EU, says the UK must regain powers on fishing, immigration and social policy, such as union law.
The Tory leadership contender told BBC Radio 4's Today programme his plan would have "benefits for everybody".
Ex-leadership rival Ken Clarke urged Mr Davis and frontrunner David Cameron not to compete on Euroscepticism.
He said most of the rights mentioned by Mr Davis had not been ceded to Europe.
But Mr Davis, the shadow home secretary, said this view was "slightly out of date", while it was "clear" there had been a "loss of power".
He suggested a referendum to demand full-scale return of power from Europe to Britain.
This would be followed by a second referendum after talks with the European Union, so voters could judge if he had delivered the goods.
The only area not up for discussion would be the European single market.
Mr Davis said the "double-lock" referendum would hold the government to account and force Brussels to take Britain seriously.
He added that the "people of Europe all have different expectations of Europe and we can't have a one-size-fits-all model anymore".
The referendums would form a "radical European policy", he said.
Other proposals put forward by Mr Davis include a new British Bill of Rights with priority over European human rights laws.
Mr Clarke told Today programme that he was "saddened" to see Europe apparently becoming an issue in the leadership election.
He said he was "inclined" to vote for Mr Cameron, but said there were still five weeks of campaigning to go.
He said his advice was that Mr Cameron should focus on other issues rather than "playing to the stereotype" of what the Conservative Party has been like over the past few years.