We did most of our shopping in Asda when we lived in Bournemouth, but did some in Lidl. We didn't buy too much because we had to carry it home. Since we moved to Bedfordshire, we use Aldi and to a lesser extent, Lidl. We top up with the odd bit from Asda. Aldi is very cheap, the meat is decent and the veg is the same as the other places. We then decided to give the nappies a go, and said that if they cause any rash or problems we would switch to something else. They turned out to be brilliant and cost a fraction, absolute fraction, of the likes of Pampers.
The stuff we top up on in Asda is stuff like ground coffee; the stuff in Aldi really isn't that nice but it's the only thing we have found that we don't really like too much.
I'd recommend Aldi to anyone to be honest. I can't imagine how much is being saved compared to the likes of Sainsbury's.