Mr Cameron’s late father was reported to be among names, including those of six British peers, three ex-Tory MPs and political party donors, named in relation to investments set up by Panamanian law firm Mossack Fonseca.
Downing St said it was a “private matter” whether the Cameron family still had funds in offshore investments and insisted Mr Cameron was in the vanguard of efforts to increase the transparency of tax deals.
But he was accused by opposition parties of failing to follow through with promises to force reform in UK crown dependencies and overseas territories which act as tax havens and faced calls for a full independent investigation.
HM Revenue and Customs has approached the International Consortium of Investigative Journalists for access to the data and said it would “act on it swiftly and appropriately” if there was any wrongdoing.
While there is nothing illegal about using offshore companies, the disclosures have intensified calls for international reform of the way tax havens are able to operate and claims of large-scale money laundering.
Mr Cameron has been a vocal advocate of reform and legislation forcing British companies to disclose who owns and benefits from their activities which comes into force in June.
Despite several years of pressure however, few UK crown dependencies and overseas territories, which are said to make up a large part of the tax havens referred to in the papers, have taken concrete action to open up the books.
He faces pressure to secure progress at an international summit on tackling corruption which he will chair in London in May and where the use of offshore tax havens to escape scrutiny will be high on the agenda.
Asked if Mr Cameron was prepared to legislate if there was continued inaction, the PM’s official spokeswoman said: “He rules nothing out. The work with them continues.”
British foreign secretary Philip Hammond, who recently met the Panamanian vice-president to discuss the issue, insisted “significant progress” was being made.
“It’s always interesting when information like this leaks because it reminds people who are up to no good how fragile and how vulnerable they make themselves by indulging in this kind of activity,” he told the BBC.
“This is a key agenda for the prime minister.”
British shadow chancellor John McDonnell said not enough had been achieved.
“Cameron promised and has failed to end tax secrecy and crack down on ‘morally unacceptable’ offshore schemes,” he said. “Real action is now needed.”
Ian Cameron’s use of the firm to help shield investments from UK tax as he built up a significant legacy, part of which was inherited by Mr Cameron, had been previously disclosed but further adds to the pressure on the PM.