The fund, based in the tax haven of Jersey, was called PMG Eagle Fund Limited and operated between 1996 and 2000.

Company documents obtained from Jersey show Ian Cameron, who operated as a stockbroker, owned 5,000 shares – a small shareholding.

Channel 4 News also uncovered further funds bearing the name PMG Eagle in the tax havens of the Cayman Islands and the Bahamas, however the secretive jurisdictions meant the ownership was not immediately available.

Mr Cameron senior has already been revealed as a director of the Blairmore Holdings investment fund based in the Bahamas, and a shareholder and the chairman of the Close International Equity Growth Fund, based in Jersey.

The existence of the third offshore fund raises more difficult questions for the Prime Minister over whether he benefited from the PMG Eagle Fund Limited in Jersey, or was an investor himself.

Yesterday, the Prime Minister admitted that he was a shareholder in Blairmore Holdings, the Panama-registered company which his father helped to establish and which is named after the Cameron family ancestral home, Blairmore House in Aberdeenshire.

Defending the fund, he stated: “If you were a UK citizen and bought units in it then you paid income tax on the dividends and you paid capital gains tax when you sold the shares.”

However, a directors’ report by PMG Eagle Fund Limited in Jersey in 1999 said the fund was designed for “long term capital appreciation” and told investors: “The Fund expects that capital appreciation will come almost entirely from increases in the value of the portfolio companies, and investors should not expect any significant benefit from dividends and interest.”

The company described itself as “a Jersey Exempt Company and is not a close company within the provisions of the UK Income and Corporation Taxes Act 1988”.

There is no suggestion that either the Prime Minister or his father evaded tax through any of these business.

The other offshore funds which bear a similar name, but which cannot be confirmed as being linked to Ian Cameron, were the PMG Eagle Fund Incorporated in the Cayman Islands and PMG Eagle Limited in the Bahamas

PMG Eagle Fund Incorporated was registered in the Cayman Islands in August 2000 before being struck-off in March 2014.

However, it is not known if Ian Cameron was also a shareholder since, as the notice of Strike Off states: “information regarding the corporate records and registers is not available for public inspection” in that territory.

PMG Eagle Limited was registered in the Bahamas, although here too information about corporate structure is not immediately available.

There has been no response yet from Downing Street in response to our questions about a third off-shore investment fund.