I don`t know shops in the UK but I would really recommand the ASUS notebooks, bought one for my wife in october and its really stunning with grafics ermmm it has a seperated 512mb vid card

thats one of my recomandations a sep vid card
But when you see the webcam results and typing on the keyboard its a pleasure to work with it.
We also have Two Packerd Hells but they are only good for scrapheap, even one off them was much more expensive then the asus.
I payed about 700 euro for the Asus X71xl laptop 17" a bit more then your 350 but I think a 15" Asus can come close to the 350 pounds.
Good luck with making your choice.
Erik