Unless you were to visit all the supermarkets in your locality, at the same time, and buy the exact same goods, it is next to impossible to prove that one outlet is cheaper than others. My sister-in-law insists that the £ shops offer good value, even after I have pointed out that they sell smaller packets of the same product, thus making comparisons almost impossible.
The easiest way to save on your weekly shop is to buy supermarket-own brand products, instead of the highly priced items. Have a look under your sink and behind your toilet. For instance, toilet cleaner priced at 30p will clean the bog just as well as Toilet Duck, at 3-4 times the price. Ditto with toilet paper !
I have been using supermarket own brand liquid detergent in my washing machine for years and it does exactly the same job as Persil.