What about Bellmans on London Road. one of those new-fangled supermarket thingys where you had a trolley and had to serve yourself?
(Across the road at Sainsburys you still had to queue at each counter for chesse, then ham, then other stuff, etc.)
Bellmans was a department store - pretty sure they didn't sell food. My grandmother used to buy her wool for knitting from there. It became Fine Fare in the early 70s - are you thinking of that? Not sure when Sainsburys moved from being a counter store to a supermarket, it was about the same time, I think.