Depending on the games you want to play you need to consider the graphics card rather than the processor. Most laptops are not really suitable for all but the most basic games.
In terms of processors, Intel recently brought out a new range of processors with the numbers i3, i5 and i7 (and different models within those numbers).
i3 are the cheapest, i5 the next, and i7 the most expensive.
For most home users an i3 is fine, but if you have the money go for an i5. An i7 will be very expensive.
You can get a low end laptop for about £300, but going up to say £400 should get you a decent laptop, though probably not good enough for gaming.