Earlier quoted context omitted.
Co-op is a UK supermarket chain and the brand used for the food retail business of The Co-operative Group, one of the world's largest consumer co-operatives. This is the Exeter branch.
There’s multiple different businesses doing business as “the co-op” in the UK IIRC, somewhat based on geography but with different branding too.
https://www.co-operative.coop/about-us/history https://www.co-operativebank.co.uk/about-us/
When a Brit talks about "The Co-op", they (we) mean the stores. The bank always has bank appended to its name.