We have Sainsbury, Tesco, Morrisons, Asda, Co-op, Aldi and Lidl all within about 6 miles of our house, so we pick and choose - certain things in certain stores. Sainsbury and Lidl are probably our favourites, with Co-op being used for convenience (it's just up the road). I have to say we have been buying more and more at Lidl's recently as they seem to just go from strength to strength. They now have in-store bakeries which are very good and so reasonably priced. Also their fresh fruit and veg is extremely good (and cheap!).
Like Pompa, we like Tesco for the fresh fish counter - last week I got a whole salmon on offer for £13.82 - I got 17 salmon steaks out of it. Now that is cheap!! But Sainsbury fresh fish is also very good. And of all of them, we've always found that Sainsbury's fruit and veg seem to have the longest shelf/fridge life.