need a pc Watch
1) Am I playing in HD, 4K, or even higher?
2) Do I feel the need to play every game on max / 'Ultra' graphics settings or am I fine with playing on high/very high or even medium?
3) Am I fine with 30 FPS or really anal about getting 60 FPS?
4) How long do I want it to 'last' before I have to start adding more, or replacing parts with more powerful parts?
5) Am I going to play in VR?
Then you also have to know what you're looking for in each part (CPU, GPU, RAM, case etc.).
That would be a much longer post, but I'll skip that as I can tell you now that trying to get a PC is a non-start for you. Assuming you 'only' want to play Cyberpunk and 2020 releases in 'just' HD at above 30 FPS with high settings, that is going to cost more than £300. Pre-built, I'm not up to date, but they seem to be closer to £1000.
I buy mostly pre-owned parts and built my own PC, which is vastly cheaper (and not particularly risky if you know what to look for and where), but even that'll still be slightly above your budget. I bought a graphics card with Cyberpunk in mind, a 980 TI, and on Ebay that cost £160. Another one that's pretty much identical but with more VRAM (so you can crank up a couple more settings) costs £40 - £50 more. This is pre-owned.
I don't see your parents denying you a PS4 but letting you have a £1000 PC for 'A Levels', nor do I see you building one yourself assuming your knowledge is zero and have it be pain-free and not annoy your parents even more. I bet if they say yes to a PC, they're gonna just buy you a £150 laptop from Argos.
I'm in year 12, and I'm trying my best to get my parents to allow me to get a gaming pc (ps4 would be 100% not allowed), since I woould be able to work on it for A-Levels, but far more importantly, Doom Eternal and Cyberpunk 2077 look beast! my budget would be about £250-£300. I don't even know how far that would even get me. I know it's "always better to build a pc" but I suck at all things computers. have been trying constantly but feel like I'm getting nowhere.
£500-600 without monitor is where you are looking imo.