Kevs right, cable greasing and moving quadrants are all important, i also believe the handbrake arm (the one that the cable connects to, it goes through the backingplate where there is a hinged T joint, with two unequal length arms coming out to the shoes) can wear where it meets the shoes.... A good trick if you have an old mini is to put clubby arms in it, there longer coming out of the backingplate, more leverage! I have trouble locking mine with 6 inch rims, I will stick some clubby arms in as soon as i can, but i fear the cable is knackered.....
So Cable must be greased, to make sure the quadrants are moving freely release the handbrake, WD40 the quadrant and get the cable either side (one hand will be "behind" the subframe gripping the cable, the other on the cable between quadrant and brake), yank it each way, more WD40 and repeat, until the quadrants are free, my left side was a bastard, i had to do this procedure at least 5 times before it freed up properly....
The way the HB works is simple, you yank the lever in the cabin, which pulls the cable, the cable routs 90 degres on the subframe, sliding through some bent over metal tabs on the subframe, then the cable turn 90 degrees again on the quadrant, except unlike the previous turn the quadrant swings with the cable, the cable is attatched to the handbrake arm we previously spoke of, the pulling force from the cable is transfered to a pusing force on the drum shoes via the t shaped lever arm.... Thats it in a nushell...
Just a thought, did you take the handbrake pins out when you adjusted the rear brakes? could impact, if you did, and you adjusted your brakes correctly and have done all the other things you mentioned and its not something silly like you have been given incorrect pads or something i could only suggest you tighten the cable a little more, get the rear wheels of the ground and get the handbrake set so you cant turn the wheels by hand on two or three clicks of the handbrake. If you cant achieve this your cable is probly stuffed or some other mechanical problem exists
Another thought, your handbrake lever (in the cabin) could be buggered, wouldn't be hard to try another and eliminate it as the cause, and wrecker that has a mini will probly have a handbrake arm to sell you for quids, also where the hanbrake mounts are welded the the floor could be snapped...
Well this is a bit incoherant... I hope you can glean something useful from it
G