After 3 years on stands, with handbrake on, the left rear brake on my 74 clubman is now stuck solid. The car is due to be picked up today on a trailer to go to a knew home.

I can't turn the adjuster, the handbrake cable isn't seized, I can move the actuator arm part that the cable connects to. I'm assuming the something has seized in the internal handbrake mechanism.

Any suggestions for how I might best approach this?

Try to get the brake drum off to see what is going on in there.

Take hammer and tap around the outside of the drum.
It sounds like the shoe has bonded itself to the drum.
If there are removal holes in the drum, you could use them to apply some force to help push the drum off.

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Find a job you love and you will never have to go to work !

Yep carefully tap all around with a BFH. Remove the two countersunks and try to move the drum back and forth whilst pulling off (well trying too!!

PS in extreme cases you may need a large puller to "coax" the drum off

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"Show me the Mini!"

Get the oxy out. Heat will fix it or xxxxx it.

Unless it's stood for a zillion years, a tap around should do it.
If not, I'd spray the adjuster with WD40 or penetrene, then warm it up with a hot air gun.

I once needed the angle grinder to cut drums off Josh's old Moke that came off a farm in Kingaroy Qld. They were seized solid.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.