LoL is not a very demanding so you can play it even with integrated graphics. Terraria's system requirements is so low you can play it on a toaster manufactured in the 1950's.
Below is LoL being play on Surface Pro 3 with a Core i5-4210u CPU and the Intel HD 4400 graphics core. The resolution is set to 1920x1080 with very high graphic settings. 17" laptops generally have 1600x900 resolution screen so performance should be better.
Below is a link to a 17" Dell for £615. If those two games are the type of games you like to play then Dell with the Core i5-4210u and the Intel HD 4400 should be more than enough for you. Hell, I even tweaked Skyrim to run decently well on a friend's laptop that only uses the Intel HD 4400. At 1600x900 resolution performance is mostly 30+ FPS outdoors and at 1366x768 resolution performance is mostly 40+ FPS outdoors.