The UK and Switzerland have signed a declaration to begin negotiations on tax issues in a step towards making Britons with Swiss bank accounts pay tax on the interest they earn.
Switzerland has strict secrecy laws and has long attracted the very wealthy as a place to save their money.
Treasury sources said negotiations were in the early stages and no details of tax rates had been agreed.
An agreement between Liechtenstein and the UK is expected to raise about £1bn.
Any agreement between the UK and Switzerland may raise more than that as there are more accounts in Switzerland.
The declaration followed talks between UK Chancellor of the Exchequer George Osborne and the Swiss Finance Minister Hans-Rudolf Merz in London.
Formal negotiations - which are expected to start at the beginning of next year - will cover the possibility of implementing a withholding tax, which would see Swiss authorities levying a tax on interest earned in their accounts on behalf of HM Revenue & Customs.
The UK would push for this to be a retrospective tax.
The UK will also push the Swiss authorities to provide more information on accounts held by UK taxpayers.
However, the Swiss government said in a statement that any agreement on information sharing would only apply from the date of the agreement, and could not be enforced retroactively.
At present, the Swiss will only provide details of interest earned by UK nationals on Swiss bank accounts if the UK tax authorities first send the Swiss complete details of the relevant accounts.
"This is a sensible and pragmatic approach by the chancellor to ensure we get money in that would otherwise not be collected," said a Treasury spokesman.
But the Treasury stressed that these were opening negotiations and that no details of tax rates, or amounts to be raised, have been set out yet.
In parallel talks, Germany has also agreed in principle to Switzerland introducing a withholding tax on the assets of German taxpayers with Swiss accounts.
Last year the G20 ordered a worldwide clampdown on offshore tax havens.