A major leak of tax documents - come to be known as the Panama Papers - have claimed that Cameron's late father Ian ran an offshore fund which avoided paying tax in Britain by hiring Bahamanian residents.
Ian Cameron's name is allegedly in the over 11 million leaked documents from the Panama-based law firm Mossack Fonseca that were passed to German newspaper 'Suddeutsche Zeitung' and shared by the International Consortium of Investigative Journalists with 107 media organisations.
Ian Cameron, who died in 2010, was a director of Blairmore, an investment fund run from the Bahamas but named after the family's ancestral home in Aberdeenshire.
The fund reportedly managed tens of millions of pounds for the wealthy.
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The fund, which was established in the 1980s, continues today and "has never paid a penny of tax in the UK on its profits" in 30 years, according to 'The Guardian.'
Blairmore Holdings was incorporated in Panama but based in the Bahamas, where the fund retained up to 50 Caribbean officers each year.
The Prime Minister's official spokesman declined to comment on whether any of Cameron's family money was still invested in the offshore fund, saying: "That is a private matter."
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"If the local government is simply going to condone this level of... Tax avoidance and tax evasion of money that has been made in Britain... Then that's (direct rule) something that has to be considered. There has to be an observance of UK tax law in those places," he told the BBC.
The broad qualification for being a tax haven is to have a low or zero rate of income tax, which offers the rich to escape paying tax owed in their own countries.
It is estimated that UK tax authorities could be losing up to 7.2 billion pounds a year from avoidance and evasion with the use of these so-called tax havens.