What I do over here, and I'm sure it'd work in the UK too, is check out the online brochure for the supermarkets before going shopping. I then work out my menus and shopping list from that. Salmon, for instance, I buy when the whole fish is on offer and I [STRIKE]fiddle with[/STRIKE] fillet it. Frozen fish and meat is usually cheaper. Smoked salmon I buy at Lidl. I go to the supermarket first thing cos here that's when you find 50% off cos they're eat that day. etc etc. We had a thread for offers I'll try to resurrect and if anyone goes somewhere, and sees an offer, post it!
On the French site I use, we did a comparison of what we now spend in the supermarket (FAR higher than before) compared to what we spent on FOOD/DRINK/SNACKS/EXTRAS before. There wasn't much difference to be honest...
The cheapest way to do this diet is to cook from scratch... buying packets of this and that always work out dearer...