You can't really find an appropriate laptop for your usage at that price point. The bottleneck of most gaming laptops will be the GPU. Mobile GPUs are notoriously expensive.
I know this may not sound like the ideal solution, but honestly, you can build a fine gaming PC within that budget. AMD CPUs are very capable with great price points. Around the £100 margin, they pretty much outperform all of Intel's offerings. But really it's all down to the graphics; and even a modest £150 can buy you a card that puts most high-end laptops to shame.
Budget games are older games or new games that won't tax a GPU - I play plenty of games on cheap laptops, and some new games scale very well down to older/budget laptops with older GPU's.
This is $654, but I'm impressed you can get a GPU in a laptop at that price (again, the 940)...sorrry, too late for me to figure out how to unscrew the link below...