Up to £3 billion is set to be raised by 2016 from UK taxpayers with money hidden in Liechtenstein, surpassing previous expectations, HM Revenue and Customs (HMRC) has said.

More than 2,400 people have registered to disclose unpaid tax since the Liechtenstein Disclosure Facility (LDF) was signed three years ago, with £363 million already paid in tax bills.

The revenue body believes the agreement over the tax haven, which was originally predicted to raise £1 billion, will produce up to £3 billion from a much larger number of people coming forward than previously anticipated.

Some 5,000 Britons are believed to have hidden away money in secret accounts in Liechtenstein and the deal allows investors who are liable to pay UK tax to "legitimise" their past tax affairs.

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.

Tax dodgers 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 agreement between the two countries was originally scheduled to run to March 2015, but has since been extended to April 5 2016.

Dave Hartnett, permanent secretary for tax at HMRC, said the LDF had been an "overwhelming success".

He said: "HMRC originally estimated the number of people who would register for the disclosure facility at 2,000, and that it would probably produce £1 billion. In light of the ongoing success of the LDF we now anticipate the arrangements will produce up to £3 billion from a much larger number of people."

Co-operation between the UK and Liechtenstein authorities was recently strengthened further by a double-taxation agreement between the two countries to ensure people are paying the right amount of tax and not being taxed twice.