Genuine AP adjuster screw and wedges(cheaper than the screw on its own).
The rear brakes on all Minis have a simple method of adjustment. A screw with 4 flattened nose points is threaded into the backplate. As this screw is turned a pair of wedges are forced against the brake shoes, which expands the shoes against the drum. This sounds simple enough and works well for a while.
The problems come from rust, wear, age and abuse. The nose of the screw gets severe grooves worn into it, making adjustment very difficult. Added to this is the corresponding wear on the wedges that work between the screw and the shoes.
Also the adjuster screw no longer has a square head so your spanner/ wrench won't grip when trying to adjust. Best solution? Replace them with this kit, includes 2 wedges and a new screw for one brake back plate.