I got my son his gaming PC from ViBox, and have found it very good. It's a 4-core AMD, GT660, 8GB machine and he gets a good gaming experience on all the games you mention. (But: he's not using two full HD screens - one HD-ready, and one SXGA.) Touch wood, it's been a good PC for a year or more now, and ViBox's support is good. Best of all, it only cost ~£450. Of course, if you may more you'll (generally) get better... ViBox have a pretty good selection of gaming systems, that go up to the kind of price you have in mind, so you wouldn't necessarily compromise on what you think you need. Maybe worth checking out.
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