If you're in Grizedale it's unlikely you'll have enough room to keep all your food in the kitchen, but they give you a nice wooden storage box under your bed, which I've found most useful.
There's a bus that goes from the bus station right to ASDA (the 6A, I believe) and they're pretty regular, so as long as you don't buy too much that you then have to lug back to campus that can be worth doing.
The only thing I ever buy on campus is milk, because everything else has about a 30% mark-up on it. It's worth planning meals ahead of time so you don't have to go and spend £3 for some cheese.
And as far as spending money on food. Sometimes I can spend as little as £6 a week, and sometimes I can be stupid and spend £50. It all depends how much you plan your shopping and what budget you have to stick to. Don't panic if you're spending too much in your first few weeks, you'll get used to cutting down your costs in your own time.
..sorry for the essay, ha.