The British Prime Minister’s late father was reported to be among figures - including six peers, three ex-Tory MPs and political party donors - named in relation to investments set up by Panamanian law firm Mossack Fonseca.
Downing Street said it was a "private matter" whether the Cameron family still had funds in offshore investments and insisted the PM was in the vanguard of efforts to increase the transparency of tax arrangements.
More than 11 million documents were passed to German newspaper Suddeutsche Zeitung and shared by the International Consortium of Investigative Journalists (ICIJ) to 107 media organisations.
British Shadow chancellor John McDonnell said the revelations were "repulsive" and demanded an investigation by HM Revenue and Customs.
The ICIJ named Conservative peer Baroness Sharples, former Tory minister Michael Mates and ex-Tory donor Lord Ashcroft as being included within the leaked documents.
It said Mossack Fonseca was used by Belize Corporate Services (BCS), a subsidiary of Lord Ashcroft’s company BCB Holdings, to provide shell corporations for its clients in 2006.
At this stage Lord Ashcroft was still a Conservative peer in the House of Lords.
Alan Kilkenny, writing on behalf of Lord Ashcroft, told the ICIJ the allegations were "completely untrue, and the events as described never happened".
He added: "The records upon which you claim to rely for those allegations either do not exist or have been falsified."
The ICIJ raised Baroness Sharples’ involvement with the Bahamas-based company Nunswell Investments Limited to make investments, although noted she did not deal with Mossack Fonseca directly when managing her company.
A law firm handling the affairs of Baroness Sharples told the ICIJ the company was registered in the UK in 2000 and now pays taxes to the British Government.
It added that the House of Lords "has been notified of Baroness Sharples’ oversight in registering her interest as a director of Nunswell Investments Limited" and that she receives "no remuneration ... nor any income or capital from that company".
Mr Mates is said to have been linked with offshore companies used for real estate development in the Bahamas.
The former minister told the ICIJ he was asked by a friend to become chairman of Haylandale Limited, with his advice sought on issues including how to deal with the government of Antigua.
According to the ICIJ, Mr Mates said he had not and would not receive any remuneration "unless and until the development took place, nor were the shares of any value", as the company "never had any real value".
There is nothing illegal about using offshore companies but 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, who will chair an international anti-corruption summit in May, has been a vocal advocate of reform and legislation forcing British companies to disclose who owns and benefits from their activities comes into force in June.
Despite several years of pressure however, few UK Crown Dependencies and Overseas Territories - 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.
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."
HM Revenue and Customs (HMRC) has approached the ICIJ for access to the data and said it would "act on it swiftly and appropriately" if there was any wrongdoing.
But the shadow chancellor said not enough had been achieved and claimed HMRC was being forced to "operate with their hands tied behind their backs" because of staffing cuts.
"The revelations in the Panama Papers are extremely serious and frankly repulsive. HMRC should treat this with the utmost priority and urgently launch an investigation," Mr McDonnell said.
Among the disclosures are:
: A suspected two billion dollar (£1.4 billion) money laundering ring run by a Russian bank and said to involve close associates of President Vladimir Putin. The Kremlin denied the president was connected to any wrongdoing and claimed he was the target of a smear operation
: Mossack Fonseca set up a company suspected of being used to launder money from the 1983 Brink’s-Mat bullion heist. A spokesman for the law firm told the ICIJ any allegations the firm helped shield the proceeds of the Brink’s-Mat robbery "are entirely false"
: Icelandic prime minister Sigmundur Gunnlaugsson reportedly had an undeclared interest in his country’s bailed-out banks and is now facing calls for his resignation
: In China the families of at least eight current and former members of the supreme ruling politburo had been found to have hidden wealth offshore, according to The Guardian
: Some 23 individuals who had had sanctions imposed on them for supporting the regimes in North Korea, Zimbabwe, Russia, Iran and Syria were said to have been revealed to have been clients of Mossack Fonseca
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 the Prime Minister, had been previously disclosed but further adds to the pressure on the PM.
There is no suggestion that this avoidance arrangement or others exposed by the leak were anything but entirely legal or that Mr Cameron’s family did not pay the UK tax due on any repatriated assets.
Mossack Fonseca said it had operated "beyond reproach" for 40 years and had never been charged with criminal wrong-doing.