Supermarkets - which one(s) did your family patronise?
As mentioned above, in my family it was Safeway for many years, from the mid 60s to the mid 70s. Then we moved over to Asda, with occasional forays to Morrison's for top up shopping. Sainsbury's didn't operate in Leeds at that time as far as I know. Neither did Waitrose. No memory of a Tesco until I moved to London. I don't recall a Co-op either, but there must have been some dotted around the place.
Local grocer's shops started signing up to Spar or Londis or similar in an effort to get access to reasonably cheap stock they could sell for not much more than the supermarkets did. Their big selling point, then as now, was that they were local, so if you suddenly realised you were running out of butter or bread, you could walk down the road to the local shop, or send a child.
When we first moved to Leeds, the local grocer's was run by a local chap, but eventually he sold out to an Asian family who I assume had not long arrived from Uganda after Idi Amin expelled all the Asian expats. Many of them had professional qualifications or high level business experience which they couldn't put to good use in the UK because of prejudice and lack of recognition of their training, so they bought corner shops, capitalising on the despair of many shopkeepers who couldn't see how to compete with the supermarkets. The new breed of shopkeepers worked incredibly hard, keeping their shops open long hours with the help of every family member, and introducing many British people to novel ingredients like unusual pulses, cumin, coriander etc (as opposed to the mass produced curry powder which had been around since Victorian times).