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.
Reaction around the world includes:
Crowds gathering outside Iceland's parliament demanding the 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 been found to have links to offshore firms
The Australian Tax Office (ATO) is investigating more than 800 individual taxpayers, all residents of Australia
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 reports
France and Spain are investigating money laundering exposed by the leaks among their resident taxpayers
Panama President Juan Carlos Varela has said his government has "zero tolerance" for illicit financial activities and would co-operate vigorously with any judicial investigation in any country
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.
Barrister Geoffrey Robertson says Britain is at the the heart of international tax avoidance
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.
Panama Papers - tax havens of the rich and powerful exposed
Eleven million 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. BBC Panorama and UK newspaper the Guardian are among 107 media organisations in 76 countries which have been analysing the documents. The BBC does not know the identity of the source
They show how the company has helped clients launder money, dodge sanctions and evade tax
Mossack Fonseca says it has operated beyond reproach for 40 years and never been accused or charged with criminal wrong-doing
Tricks of the trade: How assets are hidden and taxes evaded
Panama Papers: Full coverage; follow reaction on Twitter using #PanamaPapers; in the BBC News app, follow the tag "Panama Papers"
Watch Panorama on the BBC iPlayer (UK viewers only)
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.