Sir Vince was speaking in the wake of the release of so-called Paradise Papers, detailing financial dealings of the wealthy.
The veteran politician said in a statement: "The Paradise Papers suggest that a small number of wealthy individuals have been able, entirely legally, to put their money beyond the reach of the Exchequer.
"In the Coalition Government I introduced the register of beneficial ownership, which established who owns British companies, and sought to extend that to British Overseas Territories. This was to clamp down on tax havens operating under the British flag.
"David Cameron was initially attracted to the idea, but when the Overseas Territories said on a visit to London that they were against it, he backed down."
He added: "Given these revelations, including news that Conservative donors benefited from these arrangements, we need a parliamentary select committee to investigate fully who decided what and why. In particular, we need the release of all government papers dealing with the decision not to clamp down on off-shore tax havens.
"Only in this way can we ensure there is full public confidence in the tax system."
Labour leader Jeremy Corbyn said the disclosure "proves" that "there's one rule for the super-rich and another for the rest when it comes to paying tax."
Shadow chancellor John McDonnell added: "These are deeply worrying revelations. Despite all the Government's claims of cracking down on tax dodgers, this evidence confirms that tax avoidance is clearly continuing on an industrial scale. Either the Prime Minister or the Chancellor needs to explain how this scandalous behaviour has been allowed to go on unaddressed for so long and what action is to be taken now."
The 13.4 million documents lay bare how thousands of rich and powerful individuals invested vast sums of money in offshore fund. The papers were obtained by German newspaper Süddeutsche Zeitung.
They reveal that millions of pounds of the Queen’s private money is invested in Caribbean tax havens, a huge leak of financial documents referred to as the “Paradise Papers” has revealed.
The documents show that the Duchy of Lancaster, which manages investments for the Queen’s £520m private estate, invested around £10m in the Cayman Islands and Bermuda-based funds.
They also show that the monarch holds small investments, via funds, in businesses including off license chain Threshers and BrightHouse, which has been accused of exploiting people with mental health problems and learning disabilities in order to sell its products.
They also reveal that Donald Trump’s Secretary of Commerce, Wilbur Ross, owns a stake in a firm linked to Russian businessmen who are the subject of US sanctions.
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