The Alliance & Leicester is to close 46 branches from 1 October, affecting 310 staff, 111 of whom are full-time.
There will be fewer High Street branches
In a statement the bank said the closures would save around £5m ($9.2m) a year after it reviewed its services.
It said the decision was due to the increasing number of customers who now choose to do their banking through "direct channels" such as the internet.
Most branches that are closing are in London and the south east of England, leaving it with 254 across the UK.
Cost of £10m
The Alliance & Leicester (A&L), which reported a 12% rise in annual pre-tax profits to £525m in February, said the cost of the closures would be just under £10m.
Some 80% of A&L customers now bank directly through the internet, over the telephone or via cash machines.
It said that while "a strong branch network remains an important part of our future business model...we nevertheless are seeing a reducing number of branch transactions as our customers make increasing use of direct channels".