The Conservatives have unveiled the question which will be posed in a referendum on Britain's future in Europe if David Cameron wins the next general election.

Voters will be asked the yes-or-no question: "Do you think that the United Kingdom should remain a member of the European Union?"

The wording was revealed in a draft bill published by the Conservative Party today with the timing is designed to limit a revolt in the Commons and put pressure on the Liberal Democrats and Labour, who oppose committing now to a referendum some years away.

Download the new Independent Premium app Sharing the full story, not just the headlines

Mr Cameron is attempting to quell a growing rebellion by his MPs over Europe, after Barack Obama urged them to give the Prime Minister the space to win a better deal from the EU before Britain decides whether or not to leave it.

The draft Bill will be seen as a way to strengthen Mr Cameron’s promise of a referendum if his party wins the 2015 general election.

It is unlikely to be introduced as a government measure because the Liberal Democrats oppose the idea. But it could make progress through Parliament as a backbench Bill. A Conservative source said: “We will examine all the options to bring this Bill before Parliament, including a Private Member’s Bill, in keeping with what the Prime Minister has said.”

At least 78 MPs, including 67 Tories, have taken the unusual step of signing an amendment to last week’s Queen’s Speech regretting the absence of an EU referendum Bill. Ministers have been told they can abstain in a vote on it due tomorrow, but backbenchers and ministerial aides will be allowed to support the amendment.

If the Bill starts its passage through Parliament, Mr Cameron hopes it will “shine a spotlight” on his referendum pledge and counter the recent surge by the UK Independence Party. He also hopes the Bill will put the Liberal Democrats and Labour on the spot by forcing them to decide quickly whether they support or oppose giving the public a say on Britain’s position in Europe.

Speaking at a joint press conference with the Prime Minister at the White House, the United States President made clear that his administration would prefer the UK to remain in the EU club but said the final decision was a matter for the British people. He said: “David’s basic point – that you probably want to see if you can fix what’s broken in a very important relationship before you break it off – makes some sense to me.”

Barack Obama went on: “The UK’s participation in the EU is an expression of its influence and its role in the world, as well as, obviously, a very important economic partnership.”

Inside Politics newsletter The latest news on Brexit, politics and beyond direct to your inbox Enter your email address Continue Continue Please enter an email address Email address is invalid Fill out this field Email address is invalid Email already exists. Log in to update your newsletter preferences Register with your social account or click here to log in I would like to receive updates on politics every morning by email Update newsletter preferences

However, the President acknowledged that Mr Cameron faced “tough negotiations” over reform of the EU and stopped short of predicting success for Mr Cameron. “I would be interested in seeing whether or not those are successful before rendering a final judgement,” he said.

Mr Obama’s intervention, welcomed by Cameron aides, is significant because Tory Eurosceptics argue that the UK’s much-trumpeted “special relationship” with the US could be strengthened if Britain left the EU. In their talks at the White House, the two leaders discussed plans for a historic EU-US trade deal, which pro-Europeans hope will become a selling point for continued UK membership.

Asked how he would vote if an EU referendum were held now, Mr Cameron told the press conference: “There’s a very good reason why there’s not going to be a referendum tomorrow, [and that’s] because it would give the British public, I think, an entirely false choice between the status quo ... and leaving.”

Mr Cameron said: “Everything is driven by what is in the British national interest. That is what I’m going to deliver. It’s absolutely right for our country. It has very strong support throughout the country and in the Conservative Party and that’s exactly what I’m going to do.”

Earlier, Mr Cameron rebuked two Cabinet ministers for suggesting they would vote for Britain to quit the EU. He dismissed the question as “hypothetical” after the Education Secretary, Michael Gove, and the Defence Secretary, Philip Hammond, became the most senior Conservatives to indicate they would consider supporting Britain’s exit from the EU if a vote were held now.

The Prime Minister also criticised former Cabinet ministers, including Lord Lawson and Michael Portillo, for suggesting the UK should pull out. “The point I would make to those people is you should not give up before a negotiation has started. It seems to be an extraordinary way to go about things,” he said. “The idea of throwing in the towel before the negotiations have even started, I think, is a very, very strange opinion.”

Britain will double military support for Syrian rebels to help them withstand the “onslaught” from Bashar Assad’s regime, Mr Cameron announced. Spending on non-lethal military equipment, such as body armour and armed vehicles, is being increased this year from £10m to £20m.

Mr Cameron flew to Boston to visit the site of last month’s marathon bombings, in which three people were killed. He will fly to New York later where he will meet Prince Harry to bang the drum for British exports.