I don't know much about U.K. retailers, so I can't give you any specific recommendations. However: At your proposed budget, and with your goals, a desktop is the only way to go. It will probably need to be an AMD boxen.

"Gaming" and "laptop" are uncomfortable words to put together even when you've got a budget of thousands. On the cheap? No sir. Not a good idea. At least with a desktop you can replace the videocard with ease after a year or so if you want to give yourself a boost. A laptop is a frozen config for the most part.

Now I'll bow and shuffle away and wait for someone who knows more about U.K. sales and prices ....