Here's the stuff I've got in the past on a £10 budget because I like cooking rather than ready meals:
Value ranges at Tesco/ASDA/Sainsburys:
1kg rice 40p (egg or veg fried rice, risotto, rice with curry)
1.5kg plain flour 45p (for bread, pizza, breakfast pancakes, pastry. Can make bread with just value flour, doesn't have to be strong bread flour)
Yeast 64p (allinson dried active yeast 125g for bread & pizza)
250g lard 40p (for pastry, bread & yorkshire puddings)
1 litre skimmed UHT milk 57p (pancakes, yorkshire puddings, in tea)
400g tin kidney beans 30p (veggie stew or chilli/curry if you've got any spices in your store cupboard)
400g tin tomatoes 34p (base for stews, curry or soup; also for pizza topping)
Jar of jam 29p (on toast, in pancakes, jam tarts, good for morale)
250g butter 98p (no joke. Makes a massive difference to the pancakes, omelette, pastry, bread).
Cheapest value range tin of fruit, likely to be pineapple, peaches or grapefruit depending on the supermarket, 35p
Iceland
12 eggs £1 (boiled eggs for breakfast, egg fried rice, omelettes, to make pancakes & yorkshire puddings)
Small chicken £3 (grill the drumsticks, thighs for a pie, breast in sandwiches and in risotto, use the carcass for stock to make soup & in risotto & pie. Aldi also do a small chicken for £2.99)
Frozen mixed veg £1 (Iceland version includes sweetcorn and green beans along with the peas and carrots. Can get cheaper bags in the value ranges, but much more carrot & cauliflower).
That leaves 28p, so I might try for a loose onion, or ask at the deli counter for a really small bit of cheese (literally 30g red leicester or cheddar) which would really help with an omelette, pizza or risotto.
Definitely check what you already have, and haunt the reduced sticker sections.
Frustrating aspect is that you're unlikely to use up all the yeast, rice, jam, lard and butter in a single week, but you'll have some stuff in the store cupboard for the next week.
If you have any of the store cupboard items already, I'd go for garlic or lemon to make stuff taste of anything, or see if I could spring for a bag of value apples (90p or £1) or cheap bananas (68p for 5 in Iceland, but they don't keep as long as apples)
Recommend A Girl Called Jack's website for cheap recipes, also Frugal Queen.