Note that if you intend to play graphic intensive games then you may struggle to achieve acceptable performance and frame rates with cheaper laptops, since lower cost laptops tend to have low end integrated graphics such as Intel GMA 950 and ATI Radeon Xpress 200M.
The Samsung R40 laptop model features ATI Radeon Xpress 200M integrated graphics.
As for the processor, for £500 or less, you'll only be able to find Samsung R40 model laptops featuring a Celeron M processor. For a dual core processor, the cheapest price is around £600
A Celeron M processor will be adequate enough for surfing the net, word processing, web design and watching videos. While laptops with Celeron M processors are cheaper however, I'd avoid it, because Celeron M processors aren't as efficient in terms of power and performance compared to better processors like Core Solo, Core Duo and Core 2 Duo processors (with come with Enhanced Intel SpeedStep Technology, as well as two cores).
You can get laptops with dual core processors for as low as £370 on the net.
For a good performing gaming laptop, generally, you're going to have to spend more than £500.