You can pick up obsolete socket 775 processors on Ebay for pence - you may struggle to find a compatible motherboard and RAM though. Something like a core2 quad or even duo isn't too weak and should be okay for very light gaming.
Out of modern processors, any haswell Celeron should play most games okay (http://benchmarks-tests.com/reviews/processors/intel_celeron_g1820/gaming.php) and sets you back £35 (http://www.amazon.co.uk/Intel-Celeron-Graphics-Virtualization-Technology/dp/B00K5OJ0TS)
on the AMD side, they have recently released the budget AM1 platform, which has processors ranging from a dual core sempron for £25 to a quad core Athlon 5350 for £40. These should also lay modern games okay with a GPU and have the advantage of...