What age is the kid? Up to £800 seems excessive for a child's PC and exuberant for a teenager, or has this one left school? Will he be doing college or uni course work on it?
Personally I believe the i5's and above builds better suited to a working lad with an excessive amount of PC game titles and other uses for the PC, but for a second item to play games you can get away with a lot less if it is going to be hooked up to a 60hz 1080p display, and can be upgraded later.
You could possibly even upgrade the current PC? What are the actual specs, maybe all it needs is an SSD, new OS, GPU and PSU, maybe a case to bling it up?
Of course that is if building your own, I have three kids myself, an i3 would be more than sufficient if 4 threads are required, 8gb of memory, and with a 1080 display plenty of GPU's around £100 - £150 could do. Unless he spends £40 a week on a major title?
My lads share a PC, oldest is in high school. Below is the spec, I was thinking of a GTX 950 or 960 as they use a 1080 60hz 32" display as their GPU is pretty poor by today's standards. Apart from the GPU it works more than well enough to do anything they ask.
Asus Maximus II Gene motherboard
Q9550 LGA 775 CPU
Corsair XMS 1066 memory 4x2GB
BeQuiet cooler
Samsung EVO SSD for OS
Samsung F3 HDD for storage
Sapphire HD-4870 1GB (needs upgrading)
BeQuiet 630w PSU (overkill)
Silverstone TJ08B-E case
Windows 7 Ultimate 64bit
Cooler Master Devastator keyboard and mouse
Panasonic Viera 32" LCD TV
I was advised against changing it for a G3258 budget gaming build, and I am pretty sure it will last them a little longer, by the time they need something better I will too and maybe my current system will do them.
It certainly perked up with a fresh OS install and SSD, most old PC's can scrub up pretty well, well enough to upgrade many of the items until all that is left is a motherboard/CPU/memory upgrade to do.
With an old PC, it is also a less risky way to teach you and your kid about building or upgrading a PC.
An i3 with Hyper threading and 1080 capable GPU is all anyone not in full time employment needs, a budget gaming system is around £300 to £400.
