Axel shaft hot

George Jets said

Yep would say your axle preload on the passenger side is too tight.

Feel the center chunk if that gets hot, not just warm.

Jack it up and roll it over by hand in neutral to see what you can feel on the passenger bearing. If it's hard to turn, that's your first clue.

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On an 8 3/4" axle there's adjustment only on one side since the axles are able to slide back and forth and press on each other by the thrust button inside the differential. You'll have a hard time getting it right without a dial indicator, very difficult to tell the difference between .010" and .030" of play just by feel unless you have a lot of experience. Many times I thought it felt right and then I put my dial indicator on and it was way off.

It's a good tool with a lot of uses, you don't need a fancy expensive high-precision one either. I imagine in the UK you can find a dial indicator with magnetic stand kit for a reasonable price. May be tougher to find one in inches as opposed to metric but still, it's a fairly common tool.

This is the one I have: Summit Racing SUM-900016-1 Summit Racing™ Magnetic Base and Dial Indicator Kits | Summit Racing