Assuming you don't just have £15 left at the end of every week to spend on food, and can bulk buy then you can do it fairly easily and eat fairly well, don't buy pre prepaired stuff and buy things that will feed you more than once.
Pick up a couple of chickens from a supermarket, unless you have issues with it the halal ones are often cheaper and the quality isn't too bad for what you pay. Joint it yourself, and you can have enough for 6 meals, with 4 breasts, 4 thighs, and the carcass to make stock and you have enough for soups etc.
Pick up meat that is about to go out of date as it will be heavily reduced, especially the day before it can't be sold any more, and stick it in the freezer.
Italian food is very good for very simple, but decent food. You can rustle up a very tasty pasta dish using only olive oil, some dried chilli and a clove of garlic.
Also look for things that can be batch cooked, you can make a damn tasty bolognese, from giorgio locatelli (sp?) for bugger all, if you time it right, get into asda (or where ever) and pick up a couple of their 1kg packs of mince before they go off and are reduced down to a couple of quid, add some garlic, a couple of onions, a carrot, a stick of celery, and a litre of tomato pasata and and 1 litre of water, and your done (it wont be quite as tasty as the full recipie that calls for a bottle of red wine, but with some careful seasoning and maybe some worcester sauce it will be decent. That will make 8 servings so enough for 4 meals.
You have to get creative with a small budget as what you can get will vary, one week you may be able to pick up a load of chickens that are due to go out of date, but then the next time you go you may be able to pick up a cheap topside or something, so you have to be flexible.
Also only buy what you need when it comes to veg, yes that big bag of onions may look cheap when compared per 100g, but if you end up binning half of them then you have wasted money, if you have a local greengrocer then when you need some veg pop in there, if you only need 1 onion, then only buy 1 onion, or 2 carrots or whatever, but don't needlesly buy veg that wont get eaten, just because it looks cheaper to buy a big bag rather than nip out to buy 1 carrot.