http://www.mysupermarket.co.uk/That will allow you to compare and order from Asda, Tesco, Waitrose/Ocado, Sainsbury's. I've found that whichever one you start with tends to turn out to be the cheapest. I think it has to do with our natural tendency to look for bargains and select offers.
We like Waitrose, although we can't afford to shop exclusively from there unless we're willing to give up things like our veg box. It is upscale, but they've tried to be more budget friendly recently. Their own brand items are definitely of good quality. Some things are actually cheaper and nicer. Lots of stuff is nice but very expensive.
Tesco and Asda are pretty much similar IMO. Asda is Walmart in the UK, literally. Tesco is the UK's answer to Walmart. Sainsbury's is relatively good quality for most things, some things excellent quality. Our family has shopped here more than other places just because they always seem to be local to us. Their own brand is relatively okay, but "Basics" can be really bad sometimes. Good thing they have a fairly good return policy.
Morrisons doesn't do online, but I find them to be of good value. I don't like how they tend to have very little loose produce, but this has changed a bit in the past year or so. Somerfield/Co-op tend to be small and expensive (as in low quality for the cost), but can be handy if you don't live near another big supermarket.
I've never shopped regularly at Marks and Sparks, so I can't really say whether it's worth going there. Their ready meals are nice.
As a general rule of thumb, shops in city centres/smaller shops in a chain tend to be more expensive when you're talking about the major chains.
Then there's Aldi/Lidl/Netto/Iceland. There's Aldi in the US, so if you've shopped there you sort of know what it's like. Aldis here are similar, although they stock items geared towards British tastes. Lidl is sort of like Aldi, but stocks more national brands. Iceland is like a giant frozen food shop, although they do sell other basic stuff as well. Quality and value is a YMMV thing. Some things are excellent from Aldi/Lidl. Some things are not, and sometimes you waste a lot of money figuring out which is which.