Erm, have you actually tried running the game? You might be just fine.
The 7700 is still only a 4 core CPU, vs the recommended 8400 is 6 core. That doesn't make the 7700 sound like a big enough step if you are putting money in.
I notice the 11400F at Scan is a super price, but as in stock as the unobtainable X Box.
If you are putting money in, then given you already have DDR4 ram (and making no effort to shop around):
£270 5600X CPU
https://www.amazon.co.uk/AMD-Ryzen-5...dp/B08166SLDF/
£120 B550 mobo
https://www.amazon.co.uk/ASUS-TUF-B5...dp/B089HG351D/
There are cheaper motherboards, but probably not for your windowed case.
The bundled cooler the 5600X comes with that isn't the best, you might want to add a cheap fan:
https://www.amazon.co.uk/ARCTIC-Free...dp/B083V3L12Y/
A 5800X would nail it, but takes you over budget (and doesn't come with a fan, so that spend isn't optional).