I probably spend about £20 - £25 a week on food and I think I eat like a king, I'm always getting tasty expensive little things I don't need, could easily do it for £15 a week and have managed on £10 a week for months at a time as a student. You don't have to be vegetarian either.
There were a couple of key ingredients though...
Roast chicken: It's less than £3.50 for a big chicken (I know the poor thing was battery farmed, but when you're skint you can't be picky and you could say it's better off dead anyway so you're sort of doing it a favour

), you can get 5 or 6 meals worth of meat off one, then boil the carcass and make soup or casserole with the stock. This works best if you're sharing though or the meat goes off.
Turkey: Don't go to supermarkets for this, but find a butcher - turkey's not that popular and I used to get an enormous turkey thigh for about £1 (a week's worth of meals). This might depend a bit on your butcher though.
Offal: liver is really cheap and nutritious, if you can stomach it.
Eggs: good quality protein and loads of B vitamins. Eat one a day + something like beans and you could skip the meat.
Beans/lentils: more tasty protein
Brown rice: again, buy in bulk from indian shops, make sure it's brown 'cos you need all the vitamins you can get.
Fresh veg: onions, carrots, turnips, whatever's cheap, tinned veg (e.g. tomatoes) from Lidl can be great too
Try to buy what you need only for the next few days, or it will go off and be wasted.
Don't go to supermarkets, buy from markets instead, they're cheaper. Also, be nice to yourself and don't eat 'valu' bread or crappy cheap flavoured noodles, they're gross and you can eat much better/healthier things like brown rice or pasta instead...remember junk food is relatively expensive (50p for a chocolate bar is a lot out of a £10 budget) so try not to give in to temptation...