Mr Wheeler said voters had a "legitimate expectation" of a vote
Spread-betting millionaire Stuart Wheeler has challenged the government's decision not to hold a referendum on the EU's Lisbon Treaty.
Gordon Brown has ruled out a public vote, saying the treaty does not alter the UK's constitution.
But Rabindher Singh QC, counsel for Mr Wheeler, told the High Court: "The government promised a referendum and should keep its promise."
The government has said it is "confident" its case is strong.
Outlining Mr Wheeler's case, Mr Singh said at stake were the fundamental principles of "good administration, fair play and straight dealing with the public".
Mr Wheeler, 73, a Conservative Party donor, had a "legitimate expectation" there would be a public poll.
Mr Singh said ex-prime minister Tony Blair had promised a referendum prior to the ratification of the Constitutional Treaty, which came to nothing after plans for an EU Constitution were rejected by French and Dutch voters in 2005.
He said that promise had given rise to "a procedural legitimate expectation that a referendum would be held in respect of that treaty - and by implication any treaty containing substantially similar terms, whatever its name".
Lord Justice Richards and Mr Justice Mackay were told the evidence showed that the subsequent Lisbon Treaty and the Constitutional Treaty were all but the same, except in name.
This was backed by statements from influential figures, including Valery Giscard d'Estaing, the author of the EU Constitution proposals.
But Prime Minister Gordon Brown had unlawfully failed to honour the government's promise of a referendum, Mr Singh said.
Counsel for the office of the prime minister and the foreign secretary say Mr Wheeler's application for judicial review was brought for the "inappropriate purpose" of seeking to "change the political atmosphere" by obtaining a court judgement critical of government decisions "for use as a political manifesto".
The two-day review is being heard just days before voters in Ireland, the only EU state holding a referendum, go to the polls.
The treaty, which paves the way for greater European integration, an EU presidency and the abolition of a host of national vetoes, will effectively be killed off if Ireland votes "no" as it must be passed unanimously by all 27 states.
Mr Wheeler has raised between £160,000 and £170,000 from donors in addition to his own money to provide a fighting fund.
Ahead of the court case, he told the BBC: "I am hoping very much that the court states that the behaviour of the government in the shape of the prime minister and foreign secretary is unlawful because they promised a referendum over and over again and they have gone back on it.
"We have had a lot of support. I have had at least ten gifts of £5 from pensioners across the country."
In March, MPs voted by 346 votes to 206 to approve the EU (Amendment) Bill.
The Bill - now in the Lords - will ratify the Lisbon Treaty, which was drawn up to replace the EU constitution after that was rejected by French and Dutch voters in 2005.
The House of Lords is due to vote on calls for a referendum on 11 June.