Simon Walker said the packets handed out at the Royal Bank of Scotland and Barclays, which together paid more than 500 of their bankers more than £1m last year, were “unacceptable”.
“Thousands of people in those two companies alone earn more even than the prime minister. This is in scandal-hit companies who have had a far from successful year,” Walker told an audience of public relations executives.
The behaviour of some banks was “harming the whole of British business by focusing only on their own short-term self-interest”, he added.
Barclays was fined £290m and RBS paid £390m for rigging the LIBOR inter-bank lending rate last year while both banks were also hit by mis-selling scandals.