I've actually never bought a laptop so don't really have the necessary personal experience but the HP model listed above this post looks decent. You can get a Ryzen powered model at slightly above your budget at £549 from Curry's which has all you need and the Ryzen built in graphics aren't bad for budget gaming. 14inch screens are cheaper but it's down to what you're looking for considering it may be for long term use.
https://www.currys.co.uk/gbuk/compu...p-amd-ryzen-5-256-gb-silver-10203300-pdt.html
Looks excellent for a laptop of that price for gaming.