David Cameron offers olive branch on EU referendum as Ukip soars

David Cameron is to table his own draft bill introducing an in-out EU referendum in an attempt to douse the Eurosceptic surge within the Conservative party and in the face of a doubling of support for Ukip in a new Guardian/ICM poll.

The poll findings, showing Ukip on a record high in an ICM poll of 18%, will further unsettle backbenchers demanding that Cameron tackle the voters' lack of trust over Europe and commit to legislation in this parliament for a referendum in 2017.

The poll shows that support for the three main parties has drained away to Ukip, with each of them down four points on last month – Labour dropping to 34%, the Tories 28%, and the Liberal Democrats 11% – as Nigel Farage's party gained nine points.

For all three established parties to be falling back in the polls at the same time is unprecedented in the 29-year history of the Guardian/ICM series. The Tories are plumbing depths they have not experienced in over a decade.

The Conservatives had previously promised to publish an EU referendum bill. But on Cameron's visit to Washington on Monday, and in an attempt to respond to growing backbench clamour, Downing Street announced that the prime minister is prepared to offer formal Tory backing for a private members' bill that would guarantee a referendum.

A draft referendum bill will be published on Tuesday and Number 10 indicated that the prime minister would try to get it debated in parliament by allowing a backbencher to table it as a private member's bill. A proper government parliamentary bill cannot be introduced in the face of Lib Dem opposition. However, a private member's bill will often fail for lack of time as in practice it is relatively easy for a small group of backbenchers to use parliamentary procedure to talk it out.

A senior Tory spokesman said: "The prime minister has said he wants to explore ways in which he can make sure that [referendum] commitment is strengthened. So tomorrow the Conservative party will publish a draft bill to legislate for an in-out referendum by the end of 2017. We will examine all opportunities to bring this bill before parliament, including as a private member's bill."

Earlier Cameron – in danger of looking as weak as John Major at the height of the Maastricht crisis – took comfort from the broad endorsement of his European strategy by Barack Obama at a joint White House Press conference.

The president first described Britain's EU membership as an "expression of its influence" around the world, but then offered measured praise for the prime minister's plan to renegotiate Britain's EU membership terms after the next election. He said: "You probably want to see if you can fix what is broken in a very important relationship before you break it off – that makes some sense to me."

But Obama said he would wait to see if the negotiations succeeded before making a final judgment, and repeatedly stressed the need for the UK to be engaged.

Cameron acted on the referendum bill after it became clear that as many as 80 Tory MPs had signed an amendment, due to be debated on Wednesday, regretting the absence of a referendum bill in the Queen's Speech. In an admission of weakness Tory whips agreed that parliamentary private secretaries, the lowest rung of the government ladder, will be given a free vote. Ministers have been told they must abstain or vote against.

The Guardian/ICM poll is remarkable because barring a single month in 2002, the Conservatives have not dropped below 28% since Tony Blair's long honeymoon in 1997-98. The Lib Dems have not fallen below today's 11% in the series since September of 1997, the immediate aftermath of Blair's first victory. Labour's 34% score is its lowest since the immediate aftermath of Gordon Brown's ejection from power, in July 2010.

The poll also shows that there is a clear "Farage factor" in the personal leadership ratings. Last month voters were split down the middle on his performance with 28% saying Nigel Farage, the Ukip leader, was doing a good job, and 29% a bad job, giving a net negative score of –1. Today, the balance of opinion is running 40%:23% in his favour, a net positive of +17.

The prime minister has been infuriated by cabinet ministers Michael Gove and Philip Hammond saying on Sunday they would leave the EU if there was a referendum now. "There isn't going to be a referendum tomorrow so it is a hypothetical question," Cameron said on Monday.

He accused those predicting he will secure only inconsequential concessions from Brussels of "throwing in the towel" before negotiations have even started, and called the position held by former cabinet ministers Lord Lawson and Michael Portillo "very, very strange".

He also rejected the idea of an immediate referendum as a "false choice", adding that his plans were the best way of preserving the British national interest. He said: "There's a very good reason why there's not going to be a referendum tomorrow – it would give the British public, I think, an entirely false choice between the status quo, which I don't think is acceptable. I want to see the European Union change, I want to see Britain's relationship with the European Union change and improve. It'd be a false choice between the status quo and leaving."