I’ve just checked the rear tires on the Range Rover Sport and on the very very outside edge (nearly on the sidewall) they are down to the thread..
I’ve got 4 tyres ordered at a Tyrepro place near me so they will fit etc. They will also do a free alignment check on the Hunter machine with an additional cost if it requires adjusting.
The guy who manages the place is very knowledgeable and has done my X5 but I’m concerned about the RR as apparently it needs to be in some mode for alignment. This could be a problem as the suspension doesn’t work and it’s just always in normal mode.
What do you think?

It should be in tight tolerance mode which you should be able to do with an IDD tool but i had my Discovery 3 done when not in it and that was fine are you sure your rear wishbones are not worn as if they are get them changed first as it would be a waste to have to do it twice

I’ve no idea about the rear wishbones although one of them looks like it’s been replaced not long before we got the car. The car drives straight with no knocks or bangs.

have the bushes checked first then to see if there's any play

Pah! I had the tyres replaced yesterday and there was a lot of wire protruding from the inside edge of the rears..
Couldn't get the alignment checked as they were very busy so I'll go back in a few days.