HM Revenue and Customs (HMRC) said Thursday it had already begun criminal and serious fraud investigations into more than 500 individuals and organisations holding accounts with HSBC Geneva.
HMRC is now writing to people who have not yet come forward to give them a "window of opportunity".
The revenue and customs body is acting on information it received last year under a tax treaty, showing that more than 6,000 individuals, companies, trusts and other bodies held accounts and investments with HSBC Geneva.
A spokesperson for HSBC declined to comment on the matter when approached by AFP.
If account holders fail to come forward, HMRC added that it would launch an investigation into their affairs, which could include a criminal investigation or result in penalties of up to 200 percent in some cases.
Dave Hartnett, HMRC's permanent secretary for tax, denied the initiative amounted to an "amnesty".
"There are no special rates of penalty or interest for those who come forward voluntarily. This is an opportunity for those who have made errors in past returns to correct them," he said.
"The net is closing on offshore evaders. Don't wait for HMRC to contact you. Come forward to us and make a full disclosure."
This month, Switzerland and Britain signed an tax agreement which will allow the taxing of previously hidden funds held by Britons in Swiss bank accounts.
The agreement, which comes into force in 2013, is broadly similar to one that Swiss authorities signed with Germany.
Estimates in Britain put the amount of funds hidden by British residents in Switzerland at £125 billion ($196 billion).