HSBC Holdings Plc (HSBA) clients with accounts at its Swiss private bank in Geneva are the target of a widening investigation by U.K. authorities into alleged tax evasion, according to two people familiar with the matter.

Revenue and Customs, known as HMRC, will write to an additional 4,500 clients of the London-based bank, giving them the choice of making a full disclosure or face investigation, said the people, who declined to be named because the matter is confidential. About 800 customers have already been sent so- called Code of Practice 9 letters informing them that their tax affairs over the past 20 years will be probed, they said.

The U.K. tax authority is allocating more staff to the project as it widens the probe of Swiss bank account holders at Europe’s biggest lender, the people said. HMRC received the data from its French counterparts after Herve Falciani, a former software technician at HSBC in Geneva, stole details on at least 24,000 accounts.

Patrick O’Brien, a spokesman for HMRC in London, and a spokesman for HSBC in Geneva declined to comment.

First-half outflows from European clients were “considerable,” partly because of the data theft, Alexandre Zeller, chief executive officer of HSBC’s Swiss unit, said last month, without providing details.

The widening probe of HSBC customers comes after the U.K. and Switzerland last month agreed to settle a dispute over tax evasion by wealthy Britons holding offshore accounts with Swiss private banks. Under the agreement, customers must either make a declaration to HMRC or pay a withholding tax that also covers their past failure to disclose undeclared assets.

Under Pressure
“The price of maintaining anonymity over Swiss bank accounts for U.K. residents has been set very high,” said Mark Summers, a lawyer with Speechly Birchem in Zurich.

Swiss private banks are under pressure following a crackdown on tax evasion in the U.S. and Europe. New tax accords with the U.K. and Germany that undermine the advantages of offshore accounts may prompt clients to move money back to their home countries.

HSBC suffered an outflow of money from its private bank in 2009 after becoming aware of the data theft in the middle of 2008. The French government has used the data to search for tax dodgers and passed information on to Italian and Spanish prosecutors.

Falciani told Bloomberg News last year that he’s cooperating with French investigators and helped them pull embedded data from his laptop. The technician says he didn’t profit from the data and accepted police protection in France out of fear that account holders might try to harm him.