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."