You can probably pick up a used R9 290 for £100-£150, in fact there’s one on ebay BIN for £125. They’re new enough to be pokey but not new enough to be cool or exciting, that’s usually a good time to buy used… 600W psu should be plenty
But I’d doubt whether that’s really necessary, extreme settings can mean all sorts of madness these days- 4K HD, really high refresh rates, stuff that you won’t be able to make any use of anyway without a suitable monitor. Have you tried running it already? It’ll run on pretty much anything so the question is just exactly how good is good enough. (what you lised as minimum requirement is the recommended requirement btw!)
If you were to go on, say, Overclockers.co.uk forum you’ll find endless people with upgraditis selling last year’s hotness off for little money. It’s actually pretty difficult to tell what’s good, when you’re looking at pevious years’ kit, but OCUK is also a pretty informed site so a wanted ad that was like “need something between an R9 200 and R9 290”, you’ll probably get something.