Senior Tory MP David Davis is calling for a double referendum - one to approve a list of powers for the UK to seek to seize back and then an in/out public poll once they had been negotiated.
Mr Davis, a former Europe minister and leadership rival to Mr Cameron, said the first vote should be held within a year, before the next elections to the European Parliament in 2014.
Having a renegotiation list backed by a public vote - he predicted it would get the support of 70% of electors on a massive turnout of 90% - would be a "huge negotiating lever" in Brussels, he said.
"We have got to, somehow, dramatically change our relationship with Europe. Not a little bit of a power here and a little bit of a power there. We have got to bring back lots of powers," he said.
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