HM Revenue & Customs is expecting to generate £100m of extra tax from cases contained in the so-called Panama Papers.
The leak of data from an offshore law firm means that 66 individuals have been investigated, and HMRC has carried out four arrests and six interviews under caution.
Although the data was obtained illegally, this does not stop HMRC from using it, lawyers said.
James Badcock, from law firm Collyer Bristow, said: "The right to privacy, the freedom of the press and 'stolen data' are contentious debates.
"Some of the media are defending legal action in relation to the publication of information contained in the Paradise Papers.
"Though data may have been obtained illegally, this does not generally stop HMRC from using it to pursue taxpayers for non-compliance.
"However, the right to prevent the flow of private information is a developing area of law worldwide."
He added that there was now increased pressure on non-compliant taxpayers thanks to a raft of new initiatives alongside the data leaks and hacks.
The 'Requirement to Correct' legislation has created a deadline for taxpayers to declare offshore non-compliance by 30 September.
If this deadline is missed, HMRC can levy fines of 100 per cent to 200 per cent of the tax due and even greater penalties in some cases, with naming and shaming and potential criminal consequences.
HMRC is also receiving new information about non-UK accounts of UK residents through the new global exchange of information known as the Common Reporting Standard, Mr Badcock said.
This will make it harder than ever to hide non-compliant offshore assets, he added.
He said: "The clock is ticking on non-compliance –- taxpayers with offshore assets urgently need to decide if they need to make a disclosure.
"Even where taxpayers took professional advice on their tax arrangements, they may not have a reasonable excuse in the eyes of HMRC and the courts.
"Whether or not a taxpayer has been non-compliant, it would be extremely foolish not to go to HMRC before they come to you."
Patrick Connolly, financial adviser at Chase de Vere, said: "HMRC is making the right noises in terms of cracking down on those who abuse the tax rules.
"However, it is incredibly difficult to judge how successful they really are and many people are sceptical that they are hitting any more than the tip of the iceberg."
