The vote in parliament's lower House of Commons is not binding but is politically significant, with between 60 and 100 of the Tories' 305 lawmakers tipped to defy Cameron's direct orders for them to vote against the motion.
Defeat for the government is unlikely, because the Liberal Democrats -- the Conservatives' euro-friendly junior coalition partners -- and the main opposition Labour Party are both expected to vote with the government.
The vote comes after a stormy European Union summit on the eurozone debt crisis in which Cameron and French President Nicolas Sarkozy clashed over Britain's stance.
Cameron has imposed a three-line whip on Monday's vote, indicating Tory MPs must back the party leadership or face seeing their political careers stall. Rebels serving in the government would expect to be dismissed.
Foreign Secretary William Hague, who is strongly eurosceptic, insisted that a referendum on being in or out of the 27-member EU was "the wrong question at the wrong time", warning it would undermine the fragile British economy.
He added that the Tories wanted powers repatriated from Brussels but they were bound by the coalition government agreement struck with the Lib Dems.
"I've argued for more referendums than almost anybody else, I've argued against the euro more comprehensively than almost anybody else," Hague told BBC radio.
"But this proposition is the wrong question at the wrong time.
"It wasn't in the manifesto of either of the governing parties. It cuts right across the rules for holding referendums that we have just agreed by large majorities.
"It would create additional economic uncertainty in this country at a difficult economic time.
"Europe is undergoing a process of change and an in-out referendum people would want to know where the change was going to finish up before they voted."
A parliamentary committee ordered the House of Commons vote after more than 100,000 Britons signed a petition asking for a choice on EU membership.
Cameron has insisted he is defending Britain's interests in Europe, and at the Brussels summit on Sunday, he threatened to "exact a price" if the 17 countries who use the euro sought closer integration to deal with the crisis.
"I don't think this is the right time to legislate for an in-out referendum," the premier added.
"I think this is the right time to sort out Europe's problems, sort out the eurozone problem, defend your national interest and look to the opportunities in the future to repatriate powers back to Britain."
A row on Britain's position prompted Sarkozy to tell Cameron he was "sick of you criticising us and telling us what to do", according to British newspapers.
The prime minister's spokesman did not deny the reports in a briefing on Monday, saying: "What happens in the eurozone and in other eurozone countries matters to us, and we need to be involved in that discussion."
The issue of Europe has long been a pressure point for the Conservatives.
The biggest Conservative rebellion to date over Europe was in 1993, when 41 Tories voted against the Maastricht Treaty, an episode which proved costly to John Major's authority as prime minister.
Conservative backbencher Bernard Jenkin, among those set to vote against the government, told BBC TV: "This is basically about democracy. The British people have long wanted a referendum on the European Union.
"We haven't had one since 1975. We tried to get a referendum on Maastricht. We wouldn't be in this mess in Europe now if there had been a referendum then."