6870 -£120
http://www.overclockers.co.uk/showproduct.php?prodid=GX-205-XF&groupid=701&catid=56&subcat=1866
Very good performance for the outlay, trades blows with stock 560ti's but won't overclock as well as the 560ti.
If overclocking's not your thing then the 6870 is better value unless PhysX(it's not used in any of your listed games) is of value to you.
560ti -£156
http://www.overclockers.co.uk/showproduct.php?prodid=GX-173-OK&groupid=701&catid=1914&subcat=1810
Good clocking cards but they are sitting close to 7850 price territory and get blown away by the clocking ability of the 7850.
Nvidia 660 is inbound, depending on performance/price, it could force the 7850 down in price which could take it into your price zone, it's overbudget @£170'ish, but you get double the vram and a very overclockable gpu.