The Bank of Cyprus UK and Laiki Bank UK have both assured customers their savings are safe from the controversial eurozone bailout facing the Mediterranean country.
The move comes as the Cyprus' parliament discusses a €10 billion bailout agreed by the EU and IMF that would include a one-off levy on all Cypriot savings.
If the deal is passed by the country's MPs, up to 10% could be siphoned off from deposits in the island's banks as part of the bailout terms: 6.75% for those with less than €100,000 and 9.9% for those with more.
A spokesperson for Bank of Cyprus UK said there will be no effect on deposits in the bank as it is a UK bank, while a message on the Laiki Bank website said the bank had clarified with the Cyprus authorities their customers would not be affected.
Meanwhile, banks in the troubled country could be shut all week to avoid a run on savings, according to reports.
News of the levy has been met by alarm and condemnation from much of the international community, including Russian president Vladimir Putin who called the proposed tax "unfair, unprofessional and dangerous". There are significant Russian deposits in Cyprus' banks.