I have £200 and its a quiet environment
Do you want above neutral bass for good "fun factor"/immersion or neutral bass for maximum "competitiveness" in distinguishing foot steps?
Beyerdynamic has very good adjustment in head band so Beyerdynamic DT990 would be good for that fun bass...
Without sacrificing that much from competitiveness unlike cheap bass heavy headphones and especially closed gaming garbages do.
Looking UK pricing you could also start fitting ModMic into that budget if you need microphone.
(Beyer's design is also
easy to DIY mic mod)
With narrow head if wanting little more clamping force DT990 Pro meant for studio (coiled cable) is available for fair £100.
AKG has even better binaural soundstage "cans"/headphones, but would definitely recommend trying AKGs before hand:
That head band's "automatic adjustment" could have problems in keeping ear cups from slipping down.
Soundwise HD595 and its successor HD598 are very good for gaming.
Binaural soundstage is similar to DT990 but neutral bass makes foot steps and such more obvious.
But durability of mechanical design of this millennium's HD5xx Sennheisers isn't impressive.
While old design HD590 survived nearly ten years HD595's fashion design started decaying from weak spot after 2½ years.
And that cracking has happened all around HD5xx line up using that design.
Get some Sennheiser Hd599s and a Modmic.
HD599 apparently has more compact/"intimate" soundstage than HD598 (which is still in line up) so it wouldn't be as good for gaming:
https://homestudiobasics.com/hd-598-vs-hd-599-an-upgrade/
Gaming immersion is simply sucker for big soundstage.