Panama leaked files mention late Ian Cameron
Prime Minister David Cameron's late father Ian Cameron
David Cameron is coming under pressure to stop British overseas territories and Crown dependencies being used by the wealthy to reduce their tax bills.
A massive data leak from Panama-based law firm Mossack Fonseca showed it registered more than 100,000 secret firms to the British Virgin Islands.
Labour Party leader Jeremy Corbyn said the government needed to "stop pussyfooting around" on tax dodging.
Downing Street said the UK was "ahead of the pack" on tax transparency.
Eleven million leaked documents showed how Mossack Fonseca clients were able to launder money, dodge sanctions and avoid tax - the law firm says 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.
Leaked files also mention Mr 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.
'Honey pots of corruption'
At the launch of Labour's local government campaign, Mr Corbyn will say: "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.
"They are sucking tax revenues out of our own country and many others fuelling inequality and short-changing our public services and our people.
"There cannot be one set of tax rules for the wealthy elite and another for the rest of us."
Former Business Secretary Vince Cable told the BBC: "We do have some powers. We can't send gunboats these days but we can take the small territories under direct rule."
For three years, the UK government imposed direct rule over the Turks and Caicos Islands after evidence was found of widespread corruption among the ruling elite. It was only after it implemented rules around sharing tax information that home rule was restored in 2012.
Dominic Grieve, former Conservative attorney general, said the Tories and the coalition government had done more to close tax loopholes than the Labour Party.
Removing self governance in overseas territories was a "bit of a nuclear option" and the consequences on the people and their economy needed careful consideration, he told BBC Radio 4's Today programme.
"If the havens in overseas territories were shut down, people would go elsewhere where there might be far fewer regulations which would encourage the money laundering and criminality we want to suppress," he said.
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.
"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.