I would seriously consider using the Member's Market for this.
Prices assumed new unless otherwise stated:
Ryzen 3600 - £180.
B550 board - Get a good one, not the cheapest. Allows for future upgrades. £90.
Ram - Any 16GB 3200 or 3600 kit. £60-£80.
WD Blue 1TB NVME SSD - There are faster but makes no difference to a gamer. £87.
PSU - Aim for 600W or more to ensure future graphics upgrades £70-£80.
Case - Pick whatever as they start at £25 for naff ones, yet they all work the same - £25.
Monitor - Assuming he wants a gaming screen. It will be a 144hz VA panel. I would go for 144hz 1440p, but at £300 would be hard to get in your budget. Used is far a better choice here. £200-300.
Mouse & keyboard - The price range is huge. £50-£100.
Graphics - This is what matters most for gaming. They really are not great value at the moment. If you insist on new then you will really struggle here. A 3060Ti would be incredible, but they are £370+ and out of stock.
Speakers/headset - Assume a £20-£30 from wonderful Ebay. They will be pooh, but the budget is gone sadly.
If you buy used from the MM:
Ryzen 3600 - £150
Motherboard B450/B550 - £70
Ram - £50
Monitor - £200
This leaves £300 for a graphics card. Personally I would save up a smidge more and get either a used 1080Ti (I know it is from 2017, but it is a monster), 2060S/2070/2070S or a new 3060Ti. A 2070 sold on the MM a few weeks ago for £320. A 2060S for £300.
This brings the whole lot into the £1000-£1100 range and ensures it is powerful enough to run games at high FPS at 1440p.