Yes a fair chunk of people will have visited a supermarket of some description in the 3 days prior to testing.
Assume that they are including Little Tesco's (l know that's not their correct name) and co-ops that double as local paper shops and possibly some petrol station shops as 'supermarkets'.
Let's be honest people are hardly going to confess if they've been in touch with loads of people. Partly it because it makes them bad, and partly it means the friend will have to SI and potentially cost them money in lost earnings.
SI needs to be paid at the same rate as furlough and take into account 0 hour contacts.