Downing Street has refused to answer further questions about David Cameron’s involvement with a multimillion-pound offshore fund set up by his late father, Ian Cameron, in the tax haven of Panama.

The taciturn stance on Wednesday came after the prime minister and his aides were forced to give the fourth explanation in 48 hours about the benefit he and his family have enjoyed from Blairmore Holdings, which in 2012 was transferred from the central American tax haven to Ireland.

Questions about Cameron’s financial affairs since the publication of the Panama Papers – the biggest leak in history – has caused irritation inside Downing Street, with aides calling on critics to “put up or shut up”. On Wednesday, the London mayor, Boris Johnson described reporting of Cameron’s links to the fund as “absolute tripe”. The prime minister has previously attacked “aggressive tax avoidance”.

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But an attempt early on Wednesday to settle the matter by stating that “there are no offshore funds/trusts which the prime minister, Mrs Cameron or their children will benefit from in future”, failed to stop Labour increasing pressure on the Conservative leader.

The shadow chancellor, John McDonnell, called on the prime minister to “put the record straight rather than try to wriggle around, fooling no one”, while the Labour MP Paul Flynn said it remained unclear whether “tax-dodging paid his fees at Eton”.

So far, Downing Street’s statements have only denied any current or future benefits to the Cameron family, but that has left the prime minister exposed over the question of what they might have gained from the fund in the past.

The prime minister’s office would not respond on Wednesday to Labour’s calls for clarification on any past benefits from the offshore fund or confirm whether its latest statement denying Cameron or his family stood to benefit in future actually covered the latest incarnation of Blairmore Holdings in Ireland (although Ireland is generally treated as an offshore financial centre).

And in a sign that some leading Conservatives may not be convinced by Downing Street’s answers, Vote Leave, the leading Brexit campaign, accused No 10 of issuing a press release about a new EU referendum leaflet in an attempt to “distract the media’s attention from the issue of whether the prime minister’s family money is kept in offshore trusts”.

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In other developments from the torrent of secret company information obtained from the Panama law firm Mossack Fonseca:

• Swiss police have raided the offices of European football’s governing body, Uefa, to investigate offshore deals signed by the new Fifa president, Gianni Infantino. The Swiss attorney general’s office said the move, less than 24 hours after the contracts emerged from the leaked files, was “motivated by the suspicion of criminal mismanagement” at Uefa.

In 2003 and 2006 Infantino, then Uefa’s general counsel, signed TV rights deals with a firm controlled by Hugo Jinkis, who is now wanted by the FBI for paying bribes and kickbacks as part of a Fifa corruption inquiry. Uefa said the police were looking for copies of the TV contracts and said it was cooperating fully. Infantino strongly denies any wrongdoing and said: “For the time being, no specific individual is being targeted by these proceedings.”

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• Eight members of China’s Communist party elite whose family members used offshore companies were revealed but members of the Chinese public were unlikely to hear about them because state censors have ordered reports on the Panama Papers to be deleted, with the warning: “If material from foreign media attacking China is found on any website, it will be dealt with severely.”

• In Iceland, opposition parties pushed for the entire government to stand down after the prime minister, Sigmundur Davíð Gunnlaugsson, stepped aside on Tuesday. His wife had invested in an offshore company that held millions of pounds worth of bonds in three collapsed Icelandic banks.

• Pakistan’s prime minister, Nawaz Sharif, has responded to a storm of criticism from opposition parties about his children controlling offshore companies by announcing a judicial investigation. The move came as his sister-in-law, Tehmina Durrani, denounced offshore assets as unethical and called for the Sharif family to “simplify life drastically” and “return all foreign and local wealth to the nation”.

• Petro Poroshenko, president of Ukraine, has defended his use of a British Virgin Islands company, claiming it was “an absolutely normal procedure” to put his company into a blind trust when he became president in 2014. Opposition groups in the former Soviet state claim the move may have deprived the country of millions of dollars in tax, but Poroshenko, who is on a visit to Tokyo, said the arrangement was “absolutely transparent from the very beginning”.

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The Panama Papers were leaked to the German daily Süddeutsche Zeitung, which shared them with the Washington-based International Consortium of Investigative Journalists, the Guardian, the BBC and other media organisations.

Ramón Fonseca, founder of Mossack Fonseca, the law firm from which the 11.5m files about more than 214,000 companies emerged, has claimed his firm had not been the victim of a leak, but rather a hack and said his firm had lodged a complaint with the Panamian attorney general’s office.

The revelations have triggered official investigations in Panama and the British Virgin Islands into any wrongdoing and they appear to be adding impetus to global attempts to crack down on tax avoidance and evasion.

In Brussels, the European tax commissioner, Pierre Moscovici, said on Wednesday that much of the activity revealed in the Panama papers was “immoral, unethical and simply unacceptable” and called for the UK and other governments to drop their opposition to a European Union blacklist of non-cooperative tax jurisdictions.

A slew of figures from showbusiness, royalty and sport have also been linked with offshore companies in the documents. They included Sarah Ferguson, the Duchess of York, Margaret Thatcher’s son, Mark Thatcher, the golfer Nick Faldo, Formula 1 racing driver Nico Rosberg and Spanish film-maker Pedro Almodóvar. Amitabh Bachchan, the Bollywood superstar, denied any connection to four offshore firms saying: “It is possible that my name has been misused.”