The bankers will be punished based on their conduct, such as poor risk management, bad behaviour or a major error that might have resulted in serious financial loss for the firm.
The move by BoE comes after Lloyds Banking Group was fined £105m by the Financial Conduct Authority (FCA) for serious misconduct relating to the Special Liquidity Scheme (SLS), the Repo Rate benchmark and the London Interbank Offered Rate (LIBOR).
According to BBC correspondent Simon Jack, the new rules were among the toughest in world.
Backing the plan set by BoE, Barclays CEO Antony Jenkins said: "I believe that banks have to regulate themselves and that’s why culture is so important, so that banks do the right business in the right way.
"I would say that in principle I support the idea that where there is wrong doing, there should be appropriate punishment.
"If that’s criminal wrongdoing it should be criminal, if it’s recklessness that should be punished also, so I’m not against the concept of claw back."