The debate reignites a long-simmering row over the UK’s relationship with Europe which tore apart the Conservatives in the 1990s and which Cameron – a pragmatic eurosceptic – has tried to defuse since he became party leader six years ago.
Cameron wants the UK to remain in the EU while clawing back powers from Brussels and has ordered his party to vote against the motion.
"When your neighbours' house is on fire, your first impulse should be to help them to put out the flames, not least to stop the flames reaching your own house. This is not the time to argue about walking away," Cameron told a noisy parliament.
But MPs from all three major parties have stood up to call for giving people the chance to vote on staying in the EU, which they see as removing the UK’s sovereignty at a difficult time for the economy.
Many have said they see public anger and concern over Europe – but others have said they still intend to oppose the motion as Europe remains of critical importance to the UK.
The debate has claimed its first resignation, as Adam Holloway, Conservative MP for Gravesham, said he would no longer serve as a ministerial aide in order to support holding a referendum.
“Don't rebel against the people who sent you here,” Holloway urged MPs.
Although the vote in parliament looks set to fail and carries no legal weight, it has rattled Cameron's authority and proven an unwelcome distraction as he fights to keep Britain at the forefront of negotiations to solve the Eurozone crisis.
Right-wingers in the Conservative Party believe Cameron has toned down his position on Europe since last year's election in a concession to the pro-European Liberal Democrats, his minority coalition partner.
Some 78 members of parliament, many of them Conservatives, have put their names to a parliamentary motion calling for a referendum.