If you want to get the absolute best deals, you need to use mysupermarket and shop around (as in do more than one shop a week). As Kerri says, they don't have Morrisons, nor do they have the discount retailers like Lidl, Netto, Aldi, or Iceland.
This is my opinion based on experience shopping:
If you live in a city centre, shopping at smaller shops or even the midsized ones of a chain is more expensive than going to their bigger ones. You can sometimes get signed up to a cheap veg delivery scheme or use farm shops/farmer's markets if you are fortunate to have good economical choices near you.
The discount chains: Some have great deals. Some things are cheaper than the regular shops. Some things are more expensive. Some things the quality is good or tolerable. Sometimes the quality is awful. It's hit or miss and sometimes a matter of preference. I find Lidl's produce awful, but some people swear by it. We don't have an Aldi near us, but some of their stuff is brilliant.
The big chains-If you have a Waitrose near you, it's good to pop in to check the prices. Although they are what I'd compare to Wegman's in the US, they sometimes have good buys, especially on their "Essentials" range. This own brand range is great most of the time. We've also found good prices on odd things, so it's worth a check. Overall, your basket is probably going to be more expensive here or in Ocado (I recommend using Ocado if you plan on getting Waitrose stuff delivered) unless you buy their offers exclusively. Even then, I find it's hard to stay in budget there, but they have great stuff and good selection. Plus, Ocado is excellent to order through. If they don't have something, 99% of the time you find out before you submit your final order and on delivery day substitutions are rare. And the customer service is the best in my experience.
Sainsbury's-There are some things that you can't get anywhere else. Their Taste the Difference range is pretty good. They can be pricey. Their customer service can sometimes leave a little to be desired, and I refuse to order from them, choosing rather to shop for the few things I can't get elsewhere in the shops. Their delivery substitution thingy is crazy, and they don't have a policy to give you the same price or to make good on multibuys. Plus, they don't have a way to communicate with the grocery picker to give them instructions on substitutions, and I am pretty sure they employ surrealist artists looking for day jobs to pick your groceries. I've had some pretty bad substitutions.
Asda-UK's Walmart. Literally. So, if you don't mind giving them money, I can say they tend to be the cheapest. That's not always the best. They can be really helpful and polite. They can also be huge jerks with unclear offers. We've had things go off offer before delivery. All the other shops warn you, but not Asda. We've also had packaging break, ruining products. We don't shop here.
Tesco- UK's homegrown Walmart. We tend to shop here fairly often, but only online. I don't know what the shops are like as we don't have one near us. Tend to be cheap. You can give requests to the grocery pickers. They don't always have everything. It's really hard to explain, but their offerings are definitely different than the other shops. Maybe it's because I shopped mostly at Sainsbury's before we decided to do online shops. Generally, we are satisfied with them. Their produce tends to be better than Sainsbo's or Asda.
Local shops-Be sure to check your green grocer or butcher for deals.
