Hi, I think you will need a graphics card upgrade if anything and this will depend on your current power supply. I'll post some cards in your budget that you can look at. I'll use scan links but you can find them £5-10 cheaper elsewhere.
http://www.scan.co.uk/shop/computer-hardware/all/gpu-amd/radeon-hd-7870-pci-e-(1280-streams) - Only around 3 different ones on scan though other places such as Amazon and Overclockers have a bigger variety. http://www.scan.co.uk/shop/computer-hardware/all/gpu-nvidia/geforce-gtx-660-pci-e-30-(-960-cores) This is the nvidia alternative and you can find many reviews of these two cards together at various PC gaming reviewing websites but here's a review I found useful
http://www.pcper.com/reviews/Graphics-Cards/Frame-Rating-GTX-660-vs-HD-7870-plus-HD-7790-HD-7850-GTX-650-Ti-BOOST
Alternatively you could get a cheaper GPU and change to 8GB of RAM but 4GB is "enough" I believe in most games.