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.
Amazingly that more expensive unit has a worse GPU.
I understand you don't want to build your own PC but I'd stay away from that system builder you are looking at. It's expensive and not very well matched. (i.e. good CPU, crappy GPU).
He only starts putting in the GPUs that will allow the performance you desire around the £1000 mark (!!!??!?!).
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.