Not really a PC is it? You can’t even buy an APU of the spec in a PS5/XSX and you certainly can’t run it all from one set of unified GDDR6 (and I know people say you can’t run a CPU from that, but you demonstrably can run it well enough to run modern games).

Even just buying a GPU on the level of a PS5 (and that’s somewhere on the level of a RX 6700) is going to take nearly all your budget, leaving you maybe £100 to build the rest of the PC.

I don’t think it’s an impossible problem to solve, but you can’t do it if you’re selling a couple of thousand units.