I am really lucky that we're not really on a budget, tight or otherwise, but that being said, I make it a point of principle not to pay more than I need to for things - food included

There are only 2 of us, but even including food for the 3 cats (who eat nonstop lol), and buying local, organic produce, line-caught fresh fish etc., our grocery shopping never really goes above £50 (last time it was that high, we had bought a HUGE tuna steak that cost over £20, and split into about 6 meals lol). If we bought value fruit and veg, and frozen fish (hardly ever buy meat anyway), that would easily go below £30. And around £10/15 of that is cat food
Meal planning, and shopping around & knowing where the bargain bin is in the supermarket is the key really - I work out seven or so main meals, based around the same/similar ingredients a lot of time - so if we're making a tomato based pasta dish, I'll make double the sauce, and make another dish with it too, (just tweaking the sauce and changing the main ingredients is often enough to make them totally different!), then freeze that one for the following week (all extra portions go in the freezer too - and I double most recipes anyway, to make extra portions of each meal, to freeze - saving me money, and time spent cooking

) that way I can make sure that I always use up every last bit of food that I buy - absolutely nothing is wasted, or left to rot in the fridge! Then, we have around 3 or 4 'fresh' meals per week, and 3 or 4 meals from the freezer, with fresh veg, pasta, rice, whatever cooked at the time to go with them.
I also slow cook a LOT - it takes cheaper cuts of meat, and makes them amazingly tender, and full of flavour, and works brilliantly with veg and pulses as well. A stew/casserole that makes up to 10 portions can cost as little as £3 or £4.
I use dried beans and pulses, soaking and cooking them as required, rather than buying tins (doesn't save huge amounts, but pennies add up! and it saves on unnecessary tins, so less to recycle

), and always, always make my own sauces etc. Our herb and spice 'rack' is enormous lol.
We buy own-brand on a lot of things - cereals/biscuits/bread/frozen veggies/quorn equivalents etc. Much cheaper and 99% of the time, no-one can tell the difference. Some of them are actually a LOT nicer than the bland branded versions too!
The 'Old-style' forum on Money Saving Expert is brilliant for tips/ideas/recipes - although you would probably have to tweak them to ensure they were SW friendly.
Old Style MoneySaving - MoneySavingExpert.com Forums
I found this book recently which is really good, and might help (you can probably find it in the library, or maybe ask for it for xmas?

) It has recipes/shopping lists with receipts showing that a weeks meals for 4 ppl comes to around £25-30, and explains everything in very simple terms
How to Feed Your Whole Family a Healthy, Balanced Diet: With Very Little Money...: Amazon.co.uk: Gill Holcombe: Books
I've been doing it for years, and find that it fits perfectly with SW as a lot of it is not buying processed foods, making stuff from scratch, batch cooking etc. Plus, you'll always have a full freezer, so if you've had a bad day, are ill or simply can't be bothered to cook, you just grab something out of the freezer, and whack it in the oven or microwave, safe in the knowledge that it is homemade, healthy and either free or low-syn

(I label everything with it syns values on the different plans before I put it in the freezer, so I don't have to guess or rely on my terrible memory!)
Crikey, that was long!
HTH