David Cameron's attempt to unite his party over Europe is set to be dealt a blow today with the release of an official Treasury analysis that suggests more than three million jobs could be at risk if Britain leaves the European Union.

Calculations to be released in a speech by Danny Alexander, the Liberal Democrat Chief Secretary to the Treasury, will suggest that 3.3 million jobs are connected to Britain's membership. That disclosure is likely to infuriate Conservative Eurosceptics who insist Britain could be more prosperous outside of the EU.

Speaking in Washington on Wednesday, Mr Alexander is expected to say: “Indeed, the latest Treasury analysis shows that 3.3 million British jobs are connected to the UK's place in Europe. That is the measure of the risk that isolationists would have us take.”

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

The Daily Telegraph reported that aides to the Chancellor George Osborne are angered by the timing of the release and did not want to make public the findings contained in the Treasury analysis. The intervention is being seen as a potential Coalition dividing line over the issue of EU membership and is being seen by some as a continued Lib Dem attempts to differentiate themselves from the Tories ahead of the 2015 election.

The disclosure comes just days before the Prime Minister travels to Brussels for a clash with EU leaders over the appointment of Jean-Claude Juncker as the next president of the EU. Mr Cameron will warn them that the appointment of Mr Juncker, who is an arch federalist, would increase the chances of Britain voting to leave the EU in the 2017 in/out referendum he has promised.

Speaking in Washington on Wednesday, Mr Alexander will say that it would be “foolish to turn our backs” on the EU. “This isn't some starry-eyed, unconditional affinity for the EU. The EU has flaws and it must reform,” he will say. “But Britain can only reform it by taking our place at the table, rolling up our sleeves and getting to work. By leading in Europe, not threatening to leave it.”