Hi,
It all boils down to how FSA defines international banks. FSA categorises as European union banks and Non Eurpopean banks.
In case of Non european banks, like ICICI Bank Ltd which is Indian bank and wants to do banking in UK has to apply for a sepearte license if it wants to open branches in UK and want to do transactional banking( issuing current account, debit cards etc) in UK. If the FSA gives such license to any non European bank they are automatically covered under FSA compensation scheme of £ 50,000. ICICI Bank Ltd started subsidiary ICICI Bank UK Plc to start doing banking in UK and has a valid license of FSA to do banking in UK. all customers of this bank are protected under FSA compensation scheme- £ 50,000.
The case of european banks it is bit different. FSA and the European union has a undestanding that if either one issues a license to any bank to operate in their country , the other counterpart will not ask for seperate license. For example, if bank X gets a license from country B which is part pf european union , and now it wants to operate in UK, FSA wont issue a different license to the bank. The bank X can function with the same lincese. Under this circumsatnces, banks cover thier depositors as per the local country compensation scheme and not necessarily under FSA compensation scheme. European union compensation scheme currently stands out be approx equivalent to £ 39,000.