My top tips:
Approved food - it is a website that sells bizarre bulk things. You are best off getting together with someone else, as the boxes can be huge, and of course it depends what they happen to have in at the time, but they have been the source of many a meal at less than 1p a portion. Particulary good for ridiculously huge bags of mix to make stuff - eg just add water scones. I was aginst this at first as mixes are usually awful and expensive, but they are perfectly fine for making snacks and the cheapest thing ever.
Less fancy veg - it might seem boring, but a huge bag of potatoes, huge bag of carrots and a couple of bags of mixed frozen veg are really really cheap. I like leeks too - for some reason there are sometimes HUGE ones in the shop. Cook the veg lightly so you can still taste the flavour
Yellow stickers - every time you go to a shop, even just for a paper, check the yellow stickers. There are usually at least two areas to check - one chilled and one normal shelf. Put stuff in the freezer. We have two freezers, which sounds ridiculous (they are both in our kitchen, which is where we eat as well) but they mean we can eat so much nicer food than we could normally afford/be arsed to make
Buy dry stuff in bulk. Put in plastic containers so it doesn't go manky. Soup mix, lentils, flour, oats, sugar, dried fruit.
LENTILS. Add to all sorts. A handful in with mince doesn't change the taste but makes it go further. Just remember that lentils taste of nothing, so make sure there is actually some flavour in stuff before you put lentils in.
Alternate your shopping. I do online shop once a month at tesco or asda, then I go to Aldi one week, Iceland the next and then just the local row of shops. That way you get the best of each shop - eg Iceland is brill for things like huge blocks of cheese for cutting into smaller blocks and freezing, then using in cooking, plus frozen but not very exciting stuff like pizza, chicken nuggets etc. Aldi is excellent for tins of beans, bread, veg, foreign stuff. Local shops have bizarre short dated stuff, huge vegetables and offal.
Ooh, my best tip is to not see it as "depriving" yourselves, see it as a challenge. Me and DH are always showing off, saying "this meal was only 2p a head", "well, yesterday I cooked at 1p a head" etc and getting ridiculously excited at a bargain. It means we get to have more treats because we have saved money.
Soup soup soup. We cook up a big vat of soup every now and again, or pasta sauce - essentially enough to make about three of four times the amount we will eat at one sitting. Then freeze in small portions for lunches, quick teas, etc. Label it, or you end up defrosting the wrong thing (this happens far too regularly in our house)
Learn to mix fresh with dried/tinned/whatever. That way you still get healthy food, but you can bulk it out with cheaper stuff.
I think that's it. Oh, be always aware of what is in your fridge. So instead of thinking "what shall we have for tea, let's have x so we need to go and buy all the ingredients", think "ooh, we have x in the fridge, we could combine that with y from the cupboard and just buy z from the shop and it will be brill"