Doubt you will have a decent gaming machine under £600. Have a look at Cillblast's site, just one I picked at random. More to choose and to configure. Although a desktop keep a wary look out for size of PSU and other hardware in the specs if you're looking for a bargain from a standard manufacturer. Also keep a wary eye out on the terms they use on auction sites. A 3 GHz CPU is still 3 GHz regardless of how many cores it has.
OnePlus 5 review