The problem with this question is EVERYONE is going to have different opinions based on their preferences for food/food shopping.
We used to shop in Tesco, but they've been sneakily pushing their prices up for the past year or so, so when we moved to a different area, we switched to ASDA. ASDA, in my opinion, are cheaper for the same level of quality. If quality is something that rates second next to price (that sounds wrong, but I think you know what I mean - as in, if budget is your MOST important thing), then I would recommend ASDA easily.
We usually do a combo shop of Lidl + ASDA (and not just because they're next door to each other!). Lidl/Aldi/Netto ARE cheaper for some products so it pays to shop around, but I wouldn't do an entire weekly/monthly shop in there. I get my cheaper bits in Lidl and then everything else in ASDA.
If quality is something that is slightly more important, try Sainsbury's. They are marginally more expensive (but not by much) than ASDA but I would rate the quality of their low-end products as a bit better if that's something that's a bit more important to you.
Personally, I'd give ASDA a go for a few weeks/months and see how you like it - you may hate it and find that you prefer Tesco! It's really just so variant that you have to try it yourself and make your own decisions. Honestly, so much depends on what SORT of products you buy as different stores are better for different things.
eta: can't comment on Morrison's as we don't have one near us, but they are similar to Tesco/ASDA in price level. I find their range & variety slightly smaller, though, than those 2.