The publication of the Paradise Papers provoked strong reactions from politicians, charities and public figures around the world.

In the UK the Labour leader, Jeremy Corbyn, said the leak of more than 13 million files showed the disparity in the way tax was paid while in the US, Democrats called for an inquiry into the business links between Trump commerce secretary Wilbur Ross and a Russian firm co-owned by Vladimir Putin’s son-in-law.

The leaked documents have also made waves in Australia where the opposition Labor party has called for a comprehensive country-by-country reporting of tax data.

The Paradise Papers could help Corbyn increase pressure on Theresa May to show that she can live up to her vow to reduce inequality amid falling real wages for many Britons.

The revelations showed that there was “one rule for the super-rich and another for the rest when it comes to paying tax”, Corbyn said.

John McDonnell, the shadow chancellor, described the revelations as “deeply worrying” and said: “Either the prime minister or the chancellor need to explain how this scandalous behaviour has been allowed to go on unaddressed for so long and what action is to be taken now.

“Here we have proof that we have seen a lot of bluster from the government about tackling tax avoidance but no real action. Only last week the government was blocking Labour amendments to the finance bill to bear down on this abuse.

“Every pound avoided in tax by the super-rich is a pound desperately needed by our NHS, our schools and our caring services.”

The Liberal Democrat leader, Sir Vince Cable, called for a series of measures to combat the issue of global tax avoidance, after criticising David Cameron’s coalition government, in which he was a leading figure. “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,” the former secretary of state for business, innovation and skills said.

“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.

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.”

Meg Hillier MP, chair of the House of Commons public accounts committee, said that the government and HM Revenue and Customs (HMRC) would have to face difficult questions about the leak. “The government talks tough about clamping down on aggressive tax avoidance but once again we see HMRC being out-manoeuvred. HMRC must investigate the very worrying allegations arising from this leak. Senior HMRC officials are coming before our committee today and we will be expecting frank answers on what it intends to do.”

A government spokesperson, meanwhile, defended the Conservatives’ record on tax avoidance, stating: “Since 2010, the government has secured an additional £160bn, more than the annual UK NHS budget, for our vital public services by tackling tax avoidance, evasion and non-compliance. This includes more than £2.8bn from those trying to hide money abroad to avoid paying what they owe.

“There are 26,000 HMRC staff tackling tax avoidance and evasion, and we have provided an extra £800m to fund their efforts.”

Ana Caistor Arendar, Oxfam’s head of inequality, noted the global implications of tax evasion. “There’s an often overlooked but very real human cost to tax dodging – it deprives poor countries of billions each year needed for life-saving healthcare and life-changing education. But this is a problem that affects rich and poor countries – until leaders clamp down on widespread tax avoidance we’ll all continue to suffer.

“UK-linked tax havens such as Bermuda are at the heart of this scandal, so strong British leadership is critical to help end tax secrecy and bring global tax dodgers to book.”

Duncan Hames, director of policy at Transparency International UK, added: “Offshore financial secrecy is rotten to the core and the UK plays a disproportionately large role, ignoring what goes on in some of its crown dependencies and overseas territories, and failing to address the weaknesses in its own money laundering defences.”