Have you ever done any calculations on how much you actually save when doing "Tesco vs Iceland and Waitrose(surprise!)" comparison? When doing personal calculations and taking into account certain peculiarity of each one of them (For example Waitrose does free delivery over certain amount, will substitute items for items for the higher amount/price(for free) if selected item isn't available, give items for free if they have a short end date) I found that for me in particular online grocery shopping with Waitrose is 5-10% more expensive, while I prefer the taste of Waitrose food much more
I agree that 'free delivery' can work out costing more or about the same as paid. Have I done a proper calculation though, no. My Dad is awkward though and will convince himself he's saving money regardless.
I used to think that "discount grocery shops" are much cheaper than other grocery shops but after doing comparison for products that I buy, I found there is a little difference in price, while the quality/taste is very different.