Your problem is that you are somewhat asking the impossible.
Loss, theft, or damage is a fact of life for a laptop, at Uni. That's what insurance is for, but insurance won't replace loads of vital coursework, unless you have it safely backed up. You need an external hard drive for that, that you can keep safe. That will set you back around £70, leaving you with £330, even from your higher end.
Then, lightweight and reasonable performance, really means Ultrabook. Way outside your budget. You can get light-ish conventional laptops, but that usually means "flimsy". Not ideal for uni, either.
You really need something with an i3 processor, 4GB of RAM, and at least a 500GB hard drive. They CAN be found for £330 (just).
Your best bet is to go somewhere, like PC World (I'm not necessarily saying, buy there), and check the look, and feel, of some possibilities, that you like. Then shop around for a decent price.
You can always refer any selection, back here, for an opinion, on its quality, before you actually buy.