Mr Wheeler claims that he had "a legitimate expectation" that Gordon Brown would hold a public vote.

The Prime Minister has refused on the ground that the EU Reform Treaty (the Lisbon Treaty), introduced after proposals for a EU Constitution were voted down by the French and Dutch in 2005, did not alter the UK constitution.

But lawyers for Mr Wheeler, 73, a major Conservative Party donor, say the rejected constitution and the proposed treaty are the same in all but name.

They say the obligation to hold the promised referendum cannot be avoided simply by a name change.

The two-day case is being heard by Lord Justice Richards and Mr Justice Mackay at the High Court in London just days before voters in Ireland, the only EU state holding a referendum, go to the polls.

An Irish No vote on Thursday to the treaty – which paves the way for greater European integration, an EU presidency and the abolition of a host of national vetoes – would kill it as it must be passed unanimously by all 27 states.

Mr Wheeler, who made more than £30 million from spread-betting firm IG Index, has raised between £160,000 and £170,000 from donors in addition to his own money to provide a fighting fund.

He said in a statement that his legal team would try to prove the refusal to hold a referendum was "not only immoral but illegal, too".