[Closed] Choosing a semi integrated headset?

Recently bought a second hand carrera gryphon (disc spec) (got rid of my cannondale due to moving to a city) 😥 upon getting a second hand bike I always like to carry out a service on it and clean up anything that needs doing, upon this I noticed that the headset (cartridge bearings) are rusty and the top cartridge has a little play.

My main question is how would I know what size headset to choose, I did get in touch with Halfords (we all know what that is like?) and they no longer have the exact like for like replacement so how would I go about measuring up for one as I believe the lower cup at least looks a little smaller than the top.

Thanks in advance anyone!

Dan