The announcement of the closures comes after 82 branches were previously closed in January last year.
A provisional date of September 6 has been set for the closure of the branch on Market Place.
HSBC has said that it is closing its branches as a result of more and more customers choosing to bank online rather than in person.
The bank said that less than 50 per cent of its customers now regularly use its branch network, with footfall dropping sharply over the last five years.
The decision to close more branches is set to affect around 400 workers.
A spokesperson for HSBC has said that the bank hopes to redeploy all 400 of the affected staff to new roles, all within 15 miles of their homes.