More than 2,000 people from the UK with money invested in Liechtenstein have come forward since an agreement over the tax haven was signed in 2009, HM Revenue and Customs (HMRC) said.
The number has exceeded expectations and the revenue body believes thousands more people could make themselves known.
Some 5,000 Britons are believed to have hidden away an estimated £3 billion in secret accounts in Liechtenstein.
People who own up to what they have done could face penalties amounting to just 10% of the tax they have evaded, although they will still have to pay back taxes and interest going back up to 10 years.
Those who fail to volunteer their actions face much tougher fines amounting to 200% of their unpaid tax, as well as back taxes and interest, and in the most serious cases, prosecution.
The Liechtenstein Disclosure Facility (LDF) was signed in August 2009 and its operation has been extended for a year until April 2016.
Liechtenstein is set to implement new laws ensuring exchange of information arrangements for the first time.
Dave Hartnett, permanent secretary for tax at HMRC, said: "As the number of disclosures already exceeds the total we originally expected for the whole period of the LDF, we have agreed with the Liechtenstein government that it makes sense to extend the facility by one year to April 5, 2016."
Five biggest taxpayer stings
2,000 reveal Liechtenstein accounts
Most recently HM Revenue & Customs let Vodafone off the hook - for quite a sum. Vodafone paid out just £1.25 billion despite an original tax bill being closer to £8 billion (HMRC has always refused to reveal how much it thought the Vodafone final bill was). The episode was made even more shaming and painful because Vodafone was given several years to come good with the cash owed - even though it was sitting on a substantial cash pile at the time.
The Exchequer is estimated to have lost around £10 million to Goldman Sachs recently through an 'error' made by HMRC. The episode relates to an employee benefit trust run by Goldman allowing employees to take non-repayable loans that had no National Insurance contributions tied to them. HMRC did claw back the full amount from more than 20 businesses - but not Goldman. HMRC remains cagey about the details of the deal. Little HMRC accountability or transparency.
Huge problems with QinetiQ, the former Defence Evaluation and Research Agency, or DERA. A lack of clarity on contractual arrangements at the outset didn't help, allowing private equity company Carlyle to hammer the price down (why would you start negotiations when you didn't know the company's true value?). The Ministry of Defence behaved, it was said, like "an innocent at a table of card-sharps". Estimated cost to the taxpayer - £90 million. Huge sums were later made by QinetiQ management when the company listed.
The TaxPayers' Alliances estimates £2.7bn worth of taxpayer cash was wasted with a super-expensive 'National Programme for IT in the NHS'. The Department of Health, in the end, had very little to show for it as a consequence. Another example of poor management and a seemingly ingrained inability to provide taxpayers' with value for money.
"BT is paid £9 million to implement systems at each NHS site, even though the same systems have been purchased for under £2 million by NHS organisations outside the Programme", the Commons Public Accounts Committee noted.
Contentious. The Office for National Statistics estimated this has declined 3.4% since 1997, "with inputs increasing by 38%." The Centre for Economics and Business Research estimate that this inefficiency costs the taxpayer £58.4 billion a year.
Given the above record, are there any deals that the taxpayer has actually won out on? Not many, but the one successful project was the roll out of new Jobcentre Plus offices. It came in £314 million under budget, claims the Taxpayers' Alliance. A small cheer.