Not much. In all honesty when people say the $300 PC they're usually not counting a whole bunch of stuff. Windows will cost you most of £100 of that budget then you got the antivirus to add on to. M+K if you don't already have spares, but even then you'd likely want a better mouse. Can easily spend £100 on those too. Another £100 on the ram. We're still missing a shell, mobo, psu, cpu, gpu and hard drives at this point.
Best advice I'd say is take that budget and start to shop around the net, see what you could build with that cash. Check some benchmarks on the bits you've chosen and see where you could change parts for others and get a better PC. I do this with my builds and unfortunately it almost always ends in going over the budget to get the slightly better parts.
The fact you mentioned pounds already means you're getting screwed. Parts seem to be considerably more expensive over here.
Legit windows keys don't cost £100 and you don't need to buy an AV.