10-15% of goods in my trolley are "£5 or £2.50 for loyalty card holders". You actually have to be a member to pay correct market rates for their goods.
Your face is regularly visible on CCTV when you swipe the card. If you drive to the shop, they could easily find the number plate of the car.
This also applies to anyone who sometimes accompanies you, e.g. children.
(I don't know if this is legal or whether the do it, but the data is available.)
If you're shopping in-store in the UK, the supermarket can't profile you based on your bank card without express consent, as it falls under personally identifiable information.