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.
More top news
Five NHS trusts in the Midlands have come under fire after it emerged bosses were sitting on more than £134 million of spare cash.
A factory worker's faithful friends saved his life by lying with him to keep him warm when he fell into a diabetic coma in the freezing cold
A British military healthcare worker is being monitored at the Royal Free Hospital following a needle-stick injury in Sierra Leone.