The campaign for Britain to leave the European Union has taken a nine-point lead over the rival ‘in’ campaign, according to a poll taken since Prime Minister David Cameron set out his proposals to keep the country in the bloc.

The survey by YouGov in the Times newspaper, taken in the two days after Cameron set out his proposed changes for Britain’s relationship with the EU, represents the biggest lead for the ‘out’ campaign since the referendum wording was agreed last September.

The poll showed 45 per cent of Britons would vote to leave the bloc compared with the 36 per cent who want to remain, a nine-point gap that was up from the four-point lead the ‘leave’ campaign held last week.

Nineteen per cent said they did not know or would not vote.

A British exit would shake the Union to its core, ripping away its second largest economy and one of its top two military powers.

Pro-Europeans warn an exit from the EU would hurt Britain’s economy and could trigger the break-up of the United Kingdom by prompting another Scottish independence vote, while opponents of EU membership say Britain would prosper outside.

Cameron has spent months trying to secure a deal so that he can campaign to stay in a reformed EU. Last week he set out proposals to restrict benefits to migrants and bring more powers back from Brussels to London.

But eurosceptic members of his own party said the deal was far too weak while the country’s press dubbed the proposals a “farce”, a “joke” or a “delusion”.

If Cameron clinches a deal from other EU leaders at a summit on February 18-19 he could call a referendum as early as June 23.