I do the main part of my shop in Aldi and just pick up extra bits in Asda or Tesco. As Supergirl said, the fruit and veg is so much cheaper there and, being veggie, that's great for me! Other than that, I buy my cheese (some of their singles and cheese triangles can be used as HEA), frozen vegetables, tins (beans, tomatoes etc.), bread (Hovis wholemeal is about 80p) and I also like their under 70cal Benefit cereal bars and you can have two of them as a HEB!
If you don't have the book free branded foods book, see if you can access the SW site on your mobile. Then you can check syn values as you go. I do it all the time and it's really handy.