I'm one of those who thinks that food is more about knowledge and not necessarily budget. You can eat very healthily on the budget you describe - the war generation were on rations and there was no option to eat more crap, because it wasn't available anyway.
Oats for the morning - porridge is great and a £1 or so pack will easily last a week. You just need milk and honey or sugar to add. Fresh seasonal fruit and vegetables for a start - don't pay over the odds for something out of season. Fish - Mackerel is cheap but contains all the right oils, so too Sardines. Salmon is more expensive but every once in a while, eh? Pasta - cheap as chips, potatoes, rice (buy in bulk if you can). Eat less meat but good quality again, when you can afford it - roast a chicken yourself and keep what you don't eat for sandwiches and boil the carcass with vegetables to make soup. Beetroot is a sports food (look it up) and onion and garlic are good for the blood. Most seasonal green vegetables are invariably cheap and stacked with good stuff - if you really want to go for it, drink the water you've boiled/steamed them in (once cooled down obviously).
If you can, put aside a small amount to buy herbs, spices, stocks etc which will make your cooking more flavoursome, adventurous and worthwhile - if you buy these things all at once they're bloody expensive but worth doing in the longer run. Cooking is great fun, never a rigmarole, so learn to enjoy it and learn as much as you can about nutritious foods - and you may be surprised to learn that they're not all ridiculously expensive. On the other foot, some of the most nutritiously worthless foods and luxuries cost the Earth.