Adam Afriyie, an outspoken member of Cameron's Conservative party, told the Mail on Sunday newspaper he would tomorrow launch a bid to force a parliamentary vote in coming weeks, which would then entail a referendum next year.
He said voters did not trust Cameron's pledge to win back some powers from Brussels and then put the new terms of Britain's membership of the European Union to the public in an in-out referendum by the end of 2017.
Afriyie, a businessman who has been linked to speculation about a Conservative leadership bid in the past, wrote in the Mail on Sunday that it was in Britain's "national interest" to hold an early vote.
"In reality, the British people are unsure whether the Conservative leadership would be able to stick to its promise of holding a referendum after the election, especially if in coalition once again," he said.
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"Only by setting an early date can we kick-start EU renegotiation talks and give the British people what they so clearly want -- a say on our country's future with Europe."
Afriyie's plan involves tabling an amendment to legislation already being considered by the British parliament, which officially paves the way for the promised vote in 2017.
Cameron's Downing Street office said the amendment would not be allowed to pass "in any circumstances".
"The PM will not let it stand," a spokesman said.
The issue of Europe has plagued Cameron, who leads a coalition government with the Liberal Democrats, just as it has every other Conservative leader since the late Margaret Thatcher.
Sceptical right-wingers in the party in July forced him into backing legislation guaranteeing a vote instead of leaving it open ended. That is the legislation that Afriyie now wants to amend.
The challenge comes just days after Cameron told the annual Conservative conference that he had won European allies in his campaign to reform the EU, although he did not name them.