If you're looking for a quality laptop that provides good graphic design capabilities, a MacBook (Apple) is the way to go. Apple is used by most of the "visual arts" community as they have always had superior products and software compared to Windows based computers for graphics-based work. As far as price goes, you will be looking at £750 - £1000 for a "lower-end" one, yet it should meet your needs just fine.

http://store.apple.com/Apple/WebObjects/ukstore/