300-400 would be my price range for some something new which would be nearly double the cost of what i paid for the processor or under 300 for something used.
Playing at native resolution, or 4K with upscaling is likely to be the best image quality, so ideally that's what I'd pick: a card that can do 4K/60 native, or 4K with upscaling. The snag is, 4K is still a highly demanding resolution and especially with newer games you need a monster card to sustain decent frame rates.Testing i will accept what i can achieve, but for personal gaming i want high quality looks with as close to high performance as i can.
If you're comfortable with 4K in everything except for the very newest AAA games, then I think a card on the level of a 6750 XT or 7700 XT will do just fine, but I'll be honest that you won't achieve longer-term 4K gameplay when you'd like to spend £300-£400. As Joxeon has said, the 7800 XT is your best bet for a new card within your budget, they're really marketed for 1440p and are pretty effective at this resolution, while coping with 4K "well enough" in most games.
Nvidia does have an upscaler that tends to give you better image quality, but you'd have to pay more for a competing card, so it doesn't make sense to make the best use of your budget. For example: the 4060 Ti 16GB is also available around £400, but the 7800 XT is so much faster in raster that the 4060 Ti often needs to use DLSS just to keep up: