A consultation launched in February by Bank of England's Prudential Regulatory Authority (PRA), responsible for supervising individual banks, concluded last week.
The new rules in force require banks from outside the European Economic Area (EEA) to offer only minimal retail services.
While Bank of England declined to name the banks affected, analysts suggested that Bank of India, State Bank of India, Isbank of Turkey and Overseas Chinese Banking Corporation of Singapore are likely to be affected.
They would either have to shut down their retail banking operations in Britain or convert from branch status to full UK subsidiary - an expensive and cumbersome process.
Some American banks, including JP Morgan and Citigroup, also have UK branches, but were less likely to be seriously hit because they also operate UK subsidiaries, according to The Times.
The PRA said in a statement that deposit-taking foreign banks that want to remain a branch must have less than 100 million pounds in account balances and fewer than 5,000 customers.
The PRA consultation had suggested that the branches might be able to trade if there were a "very high level of assurance" from the regulator in the parent bank's home country.
The new rules mean it will be easier for wholesale foreign banks, which cater to other financial institutions and large corporations rather than retail customers, to open non-deposit taking branches which would not face size limits but are likely to make it very difficult for some retail bank branches to operate.
Subsidiaries are subject to more complex clearances and branches, on the other hand, are part of a home office legal entity and don't require their own capital base in the UK or a separate board.
Dion Global Solutions