The banks voiced their concerns during pre-Budget talks, according to a report in the Financial Times.
The threat of departure comes despite efforts by the government to appease banks who are becoming increasingly frustrated at the heightened bank levy and the possibility of Britain leaving the EU.
Earlier this month Citigroup announced plans to shift the head office of its European retail banking operation to Dublin from London to benefit from lower costs and capital requirements.
And HSBC has increased pressure on George Osborne to reduce the bank levy, or risk the bank moving its headquarters outside of the UK. The group is considering a move to Asia, with Hong Kong or Singapore potential destinations.
Both Credit Suisse and ING declined to comment yesterday.