Staff working at Barclays at 13 Library Place had to cut the electricity supply after the water seeped into the electrics.
The incident happened just before 9 am as staff were opening up, and Barclays said that there were no customers in at the time.
The branch remained closed for the rest of the day and ATM cash machine services there were also unavailable, however, the bank set up emergency banking services at the Post Office in Broad Street.
A spokesman said the branch would remain closed on Thursday.
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