Wealthy Britons could dodge £40bn in tax payments after the UK agreed ahead of negotiations on a tax deal with Switzerland that the country could maintain its traditional banking secrecy.

Thousands of higher rate taxpayers, who pay 50% tax on their income in the UK, will be allowed to keep their secret accounts in Zurich and Geneva and pay a low tax rate after the Treasury failed to secure agreement on sharing bank details.

Proposals to make the deal retrospective were also rejected by the Swiss authorities, saving further large sums for wealthy UK residents.

The Treasury said earlier this week that the agreement, due to be hammered out in the new year, would bring in extra revenues currently held in Swiss bank accounts beyond the reach of the UK exchequer. It is understood Treasury minister David Gauke, who will lead the negotiations, expects to raise more than £1bn.

But critics of the move said it amounted to a capitulation by the UK and showed the government was preparing to "let wealthy investors off the hook".

Richard Murphy, head of Tax Research, said: "No indication is given as to how these accounts are to be regularised. Indeed, there is no prospect they can be because the £40bn or so of evaded assets will not have to be declared by name by the Swiss. In that case there is no prospect of UK interest or penalties being charged.

"In other words David Gauke has just announced his intention to sign a total tax amnesty for UK tax evaders who have used Switzerland. Given that penalties and interest would have added well over 100% to the tax bills it is highly likely that all these evaded assets should have been due to HM Treasury. But Gauke looks like he will give away the whole lot."

Murphy is a former KPMG accountant who wrote a report for the TUC in 2008 detailing how wealthy individuals and corporations based in the UK were avoiding £25bn a year in taxes. He said losses to the taxpayer could balloon over the next few years as more people move their accounts to Switzerland's lower tax regime.

"This could have knock on effects for British banks which lose their competitive edge to Swiss banks offering the same savings rates, but much lower taxes," he said. Murphy said the agreement amounted to Gauke handing British tax sovereignty to Switzerland.

"Why should we enter a deal that denies the UK tax authority the right to make inquiries about the tax affairs of a British person? Under this agreement the Swiss are granted the right to decide how many inquiries may be made and whether they are appropriate or not."

A statement by the Swiss authorities said: "During the exploratory talks, Switzerland and the UK agreed on a lasting solution which respects the protection of bank client privacy. Consequently, the automatic exchange of information will no longer be an issue in relations between the two states.The solution will apply after the entry into force of the agreement to be negotiated (no retroactive effect)."

At the moment many UK taxpayers are faced with a choice of declaring income based offshore and paying full tax or keeping it hidden from the authorities. Under the new regime, which could levy a tax rate as low as 20%, it will become legitimate to maintain an offshore account and pay the lower Swiss tax rate.

HM Revenue & Customs has twice threatened savers with hidden offshore bank accounts with fines and penalties worth 100% of their tax bill. An amnesty in 2008 and 2009 persuaded just 10,000 of the 100,000 people with substantial offshore savings to come forward.

Approximately £100bn–£125bn of British investors' money is believed to be in Swiss banks.

MEP Sharon Bowles, who chairs the European parliament's influential economic and monetary affairs committee, welcomed the deal but said she was concerned it lacked a retrospective element. She warned that Europe faced a €250bn (£223bn) tax fraud bill every year that governments must tackle.