David Cameron faces yet more questions today after four public denials over his family’s tax affairs failed to halt concerns about whether he had previously benefited from an offshore fund set up by his late father.

Labour MPs demanded more answers after a frustrated Downing Street failed to make clear if the prime minister had gained in the past from Blairmore Holdings, which was set up by Ian Cameron in Panama.

Cameron also came under scrutiny after it emerged he had lobbied against a key EU reform to reveal the identity of people behind offshore trusts. He wrote to EU officials saying there were “important differences” between trust and shell companies and warned that plans for a public register of company ownership may not “be appropriate generally”, the Financial Times reported.

In article today for LabourList shadow Cabinet minister Jon Ashworth criticised Cameron’s “partial statement” and asked whether Downing Street press officers were “playing for time and playing dumb”.

“First they went on the defensive saying the Prime Minister’s tax affairs were a private matter. Then as pressure mounted, Cameron made a partial statement saying neither he nor his family benefit from offshore trusts. When many questions remained about whether they had benefited in the past or would benefit in the future they gave another statement saying they would not benefit ‘in the future’, but gave nothing away about benefiting in the past.”

John McDonnell, the shadow Chancellor, has called on Cameron to “put the record straight rather than try to wriggle around, fooling no-one”.

Paul Flynn, a Labour backbencher, said it is still unclear to voters as to whether “tax-dodging paid his [Cameron’s] fees at Eton”.

Richard Burgon, shadow City minister, said Cameron’s intervention to block increased EU transparency of offshore trusts, showed what was in the Tories’ “heart of hearts”.

“The Prime Minister can’t raise a finger to save our steel industry but at the drop of a hat he can personally intervene to undermine EU efforts to clamp down on tax avoidance.

“When things like this come out from the very top of the Conservative Party it completely undermines anything they have said previously on this major issue.

“It’s time that they treated tax avoidance as the serious matter people across Britain know it is.”

Boris Johnson yesterday described the claims about Cameron’s family as “absolute tripe”.

An angry Downing Street told critics of the Cameron’s financial arrangements to “put up or shut up”.

In its fourth statement on the issue, yesterday, Downing Street officials said: “There are no offshore funds/trusts which the prime minister, Mrs Cameron or their children will benefit from in future.”

They did not elaborate on what had happened in the past.