Jeremy Corbyn has suggested the Queen, among others, should apologise for using overseas tax havens if they were used to avoid taxation in the UK.
The Labour leader was asked at the CBI conference whether the Queen should say sorry for making overseas investments.
He said anyone putting money into tax havens for the purposes of avoidance should "not just apologise for it, recognise what it does to our society".
The BBC has revealed that the Queen's estate has used overseas tax havens.
It comes after a leak of confidential papers from Bermuda revealed the secret offshore investments of the rich and famous, including the Queen.
Mr Corbyn's spokesman later clarified his comments, saying the Labour leader did not specifically call on the Queen to apologise but thought "anyone who puts money into a tax haven to avoid paying tax should acknowledge the damage it does to society".
Mr Corbyn called for a full inquiry, public lists of company ownership, and a new tax enforcement unit to tackle tax evasion.
Buckingham Palace has not commented on the revelation that the Duchy of Lancaster, which handles the Queen's private wealth, used offshore investments.
A spokesperson for the Duchy of Lancaster said: "We operate a number of investments and a few of these are with overseas funds. All of our investments are fully audited and legitimate.
"The Queen voluntarily pays tax on any income she receives from the Duchy."
HMRC chief executive Jon Thompson vowed to "chase down" anyone trying to hide money offshore and evade tax.
He told the Commons Public Accounts Committee that HMRC had asked to see the leaked Paradise Papers in order to "look at every case of tax evasion very seriously".
Mr Thompson said there were 66 ongoing criminal investigations into the Panama Papers, which in April 2016 exposed tax avoidance and evasion, saying £100m could be retrieved.
"That gives you some sense about how long quite complicated tax cases take to bring to some sort of fruition," he added.
Theresa May insisted efforts were already under way to obtain revenue from offshore tax vehicles, adding: "We want people to pay the tax that is due".
At the CBI conference, the prime minister said HMRC had collected £160bn by tackling tax avoidance, evasion and non-compliance since 2010.
Mrs May's spokesperson said: "It is important to point out that holding investments offshore is not an automatic sign of wrongdoing, but HMRC has requested to see the papers urgently so it can look into any allegations."
But when asked, Mrs May did not commit to a public inquiry into tax revenue lost through offshore tax avoidance schemes.
Among the Paradise Papers documents was evidence that Tory donor Lord Ashcroft remained a non-dom and continued to avoid tax despite attempts to make peers pay their full share.
Lord Ashcroft has insisted he did not ignore rules in relation to the Punta Gorda offshore trust and said his tax residency was "publicly available information".
The leaked documents show that between 2000 and 2010, Lord Ashcroft received payments of around $200m (£150m) from his offshore trust in Bermuda.
Responding to the programme, Lord Ashcroft wrote: "At no point has it been suggested directly to me, or through others, that I have taken any inappropriate action."
He also explained why he ran away from a Panorama reporter who approached him for comment, taking refuge in a toilet, saying he was "determined" not to "fall victim to their ambush".
The Paradise Papers puts into question the practice of using highly secretive offshore tax havens, which is legal.
Bermuda's premier David Burt said the territory has a "robust regulatory regime" with the same tax system in place since 1898. He added the UK's tax law allows the use of offshore tax havens.
Former Business Secretary, Sir Vince Cable, criticised the government for not clamping down on offshore tax havens trading under the British flag.
He said: "The Paradise Papers suggest that a small number of wealthy individuals have been able, entirely legally, to put their money beyond the reach of the Exchequer."
The papers are a huge batch of leaked documents mostly from offshore law firm Appleby, along with corporate registries in 19 tax jurisdictions, which reveal the financial dealings of politicians, celebrities, corporate giants and business leaders.
The 13.4 million records were passed to German newspaper Süddeutsche Zeitung and then shared with the International Consortium of Investigative Journalists (ICIJ). Panorama has led research for the BBC as part of a global investigation involving nearly 100 other media organisations, including the Guardian, in 67 countries. The BBC does not know the identity of the source.
Paradise Papers: Full coverage; follow reaction on Twitter using #ParadisePapers; in the BBC News app, follow the tag "Paradise Papers"
Watch Panorama on the BBC iPlayer (UK viewers only)