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.
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.”
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.
During his speech, Mr Corbyn is also expected to call for HM Revenue and Customs (HMRC) to be given more resources to tackle tax dodgers.
HMRC says it has been at the forefront of efforts to improve international tax transparency.
Using offshore companies is not illegal, but this leak has intensified calls for more transparency and reform.
HMRC said information it had received on offshore companies was the subject of “intensive investigation” and this data would be acted on “swiftly and appropriately”.
Mr Cameron has come under further pressure following the leak over his late father’s business affairs.
Ian Cameron was among those named in relation to investments set up by Mossack Fonseca.
Downing Street said the issue of whether the Cameron family still had funds in offshore investments was a “private matter”.
Dominic Grieve said he understood Mr Cameron had no shares in offshore companies, adding there was a need for transparency among public figures.