The outlet, in Halford Street, Leicester is one of 37 Britannia branches which are being shut nationally by Co-operative Bank, which merged with Britannia in 2009.
The Co-operative Bank said it was closing Britannia branches where there was a Co-operative branch close by – in this case in Market Place.
It is re-branding all remaining Britannia branches under the Co-operative banner.
A spokesman for the Co-op said the only jobs losses at the Halford Street business, which employed 17 people, were at managerial level, while its customer service staff had transferred to the Market Place branch.