Prime Minister David Cameron has come under pressure to check the usage of British overseas territories and crown dependencies by the wealthy as tax havens.
A massive data leak from Panama-based law firm Mossack Fonseca showed it registered more than 100,000 secret firms in the British Virgin Islands.
Labour Party leader Jeremy Corbyn said the government needed to "stop pussyfooting around" on tax dodging.
Downing Street said Britain was "ahead of the pack" on tax transparency, BBC reported.
At least 11 million leaked documents showed how Mossack Fonseca clients laundered money, dodged sanctions and avoided tax -- the law firm said it has operated beyond reproach for 40 years.
There are links to 12 current or former heads of state in the data, including dictators accused of looting their own countries.
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The leaks have gained worldwide attention and reactions, with crowds gathering outside Iceland's parliament demanding Prime Minister Sigmundur Gunnlaugsson step down over allegations he concealed investments in an offshore company.
Close relatives of seven current or former Chinese leaders have also been found to have links to offshore firms, the papers said.
The Australian Tax Office (ATO) is investigating more than 800 individual taxpayers, all residents of Australia, following the leak.
The US Department of Justice is reviewing the leaked documents to look for evidence of corruption that could be prosecuted in the US, the Wall Street Journal reported.
France and Spain are also investigating money laundering exposed by the leaks among their resident taxpayers.
Panama President Juan Carlos Varela has said that his government has "zero tolerance" for illicit financial activities and would co-operate vigorously with any judicial investigation in any country.
Leaked files also mentioned Cameron's late father, Ian Cameron, who used one of the most secretive tools of the offshore trade after he helped set up a fund for investors.
At the launch of Labour's local government campaign, Corbyn said: "It is time to get tough on tax havens. Britain has a huge responsibility. Many of those tax havens are British overseas territories or crown dependencies."
"As the leaked documents show, tax havens have become honey pots of international corruption, tax avoidance and evasion," he said.
"There cannot be one set of tax rules for the wealthy elite and another for the rest of us."
Geoffrey Robertson QC, an international human rights lawyer, said: "The British Empire has shrunk largely to a number of tax havens -- treasure islands, as they are known."
"Britain is at the heart -- the hub -- of international tax avoidance by allowing these little remnants of empire to have tax secrecy laws and enable offshore trusts and offshore companies to operate without transparency," Robertson said.
"These little countries are endowed by international law with sovereignty. They can set up their own regimes which promise utter secrecy and have no transparency."
He said change could come with "some form of international convention" to require transparency, lawyers reconsidering their ethics and an international enforcement body able to inquire, inspect and punish.
The documents held by the Panama-based law firm Mossack Fonseca have been passed to German newspaper Sueddeutsche Zeitung, which then shared them with the International Consortium of Investigative Journalists.