Minis today mostly still have brake drums on the rear with the square brake adjuster wedge and two brake adjuster tappets, one either side, to adjust the rear brake shoes. The square on the adjuster wedge can snap off or become rounded if the wedge siezes. One answer to this is to weld a nut on it. This allows you to use a larger spanner to adjust it. The heat from the welder will also free off the siezed adjuster wedge. If you do not weld and can remove the wedge you can replace it with a new one.

In order to avoid further siezure cut a small piece of tube, similar in diameter to the brake adjuster wedge’s thread. Slit it down the side, cover the brake adjuster threads with copper grease and slide the slit tubing over them. This will help to stop it siezing in future.