thread the last part is certainly true
the tesco problem is tricky, even with the perfect app, a single member of staff getting it would need thousands of people tested, the number of false positives would likely just make people not use the app.

though I guess some measure of "time spent" and "riskiness" could be worked out eventually... eg, it would alert other employees to get tested, but maybe only tell customers to keep an eye out for symptoms. but how would the app know you were in tesco and not in someones flat above it.
permalink time spent in the general location,
how much you moved about? any flat is going to be smaller than the floorplan of a supermarket. however, visiting a friend that lives over a corner shop would be harder to differentiate
permalink I guess it they are working on bluetooth like the
apple one it's probably easier... but that doesn't track geographical data so less useful to pick up problem locations.

block of flats would seem a problem for anything that relies on GPS.