Again, maybe England is different, but we have this sort of thing here for large chains, there is a site called mysupermarket.co.uk that will take your shopping list and tell you which supermarket is cheapest.
Why would a small store (the sort that aren't already engaged in this sort of thing) willingly signup to be pitched against their competitors in a race to the bottom? It's nonsensical. My mother shops at specific stores for specific goods because over the years of custom she has had a good experience with their pricing and service, she views the good experience she's had as justification for not shopping around, "they've always been good to me so spending time looking around at new shops to maybe save 2% isn't worth it" but if she could just type "umbrella" into a website and instantly be told which shop is the best for that item she'd no longer be loyal to that shop.
Retail isn't the hackernews world of SaaS, people don't choose to spend an extra 20% every time because "it's a good brand", "the founders are good people", they choose primarily based on price and service is a small part of it, a part most people will sacrifice to save 10%.