One of the Tories' biggest donors was signed up to a tax avoidance scheme that also included comedian Jimmy Carr, the Observer has established.

The revelation is intensely embarrassing for David Cameron, who attacked the comic's use of such schemes as "morally wrong".

Records at Companies House reveal that George Robinson, a hedge fund manager who has given the Tories more than £250,000, was – in the 12 months leading up until 21 January 2010 – a director of a company called Romangate. The Times reported last week that Romangate, which had more than 500 directors, including Carr and Robinson, was part of a tax avoidance strategy called Rushmore. The scheme was closed down in 2009, before its members could claim any tax relief, following an investigation by HMRC.

The scheme was thought to be legitimate when it was set up. However, the then treasury secretary, Stephen Timms, told parliament that the strategy was a "highly abusive, completely contrived arrangement" that "was set up with the sole aim of avoiding paying the tax due to the Exchequer".

Robinson, who has an estimated wealth of £215m and whose Sloane Robinson hedge fund earns millions for its members, has donated money to a number of good causes. There is no suggestion that he benefited from being a director of Romangate because the company was closed down before any tax relief could be claimed.

However, his links to the scheme are likely to trigger awkward questions for Cameron and ensure that the issue of tax remains at the top of the political agenda. It will also raise questions about Cameron's judgment in seeming to single out Carr for criticism by questioning the comic's decision to put his money into "very dodgy tax-avoiding schemes". The prime minister has come under fire for refusing to be drawn on separate claims that Gary Barlow of Take That put his money into a separate, legitimate scheme to avoid tax. Barlow campaigned alongside the Tory leader at the last general election and Cameron's refusal to condemn the singer has drawn criticism.

Senior Tories have accused Cameron of "shooting from the hip" while critics have accused him of partisanship. "If only Jimmy Carr has given £50 to the Tories, Cameron would have had to pull his condemnation," joked Lord Oakeshott, the former Lib Dem Treasury spokesman. A spokesman for the prime minister denied that Cameron had singled out Carr, saying that his attack was on the comic's use of a particular tax avoidance scheme, known as K2, rather than the man himself. He declined to comment on what, if any, views the prime minister held on Robinson's involvement in a tax avoidance scheme criticised by HMRC.

Robinson, a trustee of the Policy Exchange thinktank, has given £256,000 to the Tories since 2004, according to donations registered with the Electoral Commission. On 30 September 2010, he gave £54,000, and a further £50,000 last October.

The size of the donations would entitle Robinson to attend prestigious party events. An annual donation of £50,000 entitles donors to membership of the elite Leader's Group. The party's website explains: "The Leader's Group is the premier supporter group of the Conservative party. Members are invited to join David Cameron and other senior figures from the Conservative party at dinners, post-PMQ lunches, drinks receptions, election result events and important campaign launches."

The issue of tax is likely to dog the Tories in coming weeks. Next month the Lib Dems are launching a tax working group that will develop new policies to distance themselves from their coalition partners at the next election.

Oakeshott called on the Tories to address one matter urgently. "Non-doms is a big issue," he said. "What are they going to do about it?" Richard Murphy, a tax expert, predicted that the focus would now switch from individuals' tax affairs to big business. "Jimmy Carr has apologised, but if we were to expose the use of tax havens by multinationals they would change their behaviour too," Murphy said.

A Conservative party spokesman said: "We are not going to give a running commentary on the tax affairs of others. All donations to the Conservative party are properly and transparently declared to the Electoral Commission." Robinson's secretary confirmed that he was aware of requests from the Observer for a comment, but calls to the financier's office were not returned.