No it still has only an entry level graphics card a £800 gaming PC should have a £150-£200 graphics card not a £75 one, look for at least a Radeon 7850 and an i5 CPU. You can custom build on this site http://www.computerplanet.co.uk/index.html they are not amazing value but are better than those ones you found on Ebay.
Has a GTX 570 and an Ivybridge CPU. Should get you some decent performance in BF3. NOTE: The CPU/mobo is not designed for overclocking so if you plan to do that you'll want to consider a K CPU and z77 mobo.