Michael Shanly, whose fortune is estimated at around £157 million, pleaded guilty to the charges earlier this week.
Shanly's prosecution, which will mean him paying almost double the £430,000 or so of inheritance tax he was trying to avoid, was based on information apparently stolen from HSBC's Geneva branch by a former employee in 2010.
However, HMRC hopes that it is the first of many such cases that it will be able to bring since launching a crackdown on rich tax dodgers with offshore accounts last year.
The initiative involves an agreement between the UK and tax haven Switzerland, which means that Britons holding offshore accounts with Swiss private banks must now either make a declaration to HMRC or pay a withholding tax that also covers their past failure to disclose undeclared assets.
This is a break with tradition, as it is the first time that Switzerland has formerly agreed to provide information about Britons with Swiss bank accounts.
There is still a long way to go to reach HMRC's target of £35 billion in extra tax, though. It said: "HMRC criminal investigators continue to review the information, and further prosecutions are likely."
Tax experts in London are therefore warning that any UK taxpayers who still have undeclared sums in overseas accounts should view the Shanly prosecution as a wake-up call.
John Cassidy, a tax investigation and dispute resolution partner at accountant PKF, said: "The prosecution sends out a strong message to anyone with hidden assets in offshore accounts.
"HMRC will do all it can to catch you if your tax affairs are not in order, whether through deliberate deception or through ignorance of your tax obligations."