All the single line .70" bore brake master cylinders as used on the Mini are NOT the same! They may look and function the same but some used an upper "cup" seal and some used and upper "ring" seal. This is for masters using the upper ring seal.
For the upper cup seal kit see 8G8689.

This kit includes the rubber parts need to rebuild a GMC159 master cylinder.

Brake master cylinder repair kit for GMC227 dual line master cylinder 1985-88 with yellow identity band. This kit will not fit later brake master with servo built in as fitted from 1988 on

Master Cylinder repair kit fitted for repairing the late master cylinder that was attached to the servo from 1995 until the end of production. Similar to GRK1032, but uses a longer seal in conjunction with a nylon bearing.

One of the brake master cylinders used on some of the later model Minis is a GMC242, now GMC90376. If you decide that rebuilding it is the best option, then this seal kit includes all the internal rubber bits you will need to do the job right. Very inexpensive compared to the price of new master cylinder!

Almost every Mini built prior to the dual circuit system uses a .70" bore master cylinder. This kit fits all .70" bore, single line brake masters that use a "cup" seal for the top seal. The original size in the '59-'64 Mini was .75" but as most of these cylinders have been replaced with the .70" size it is best to check the very early models.
See GRK1006 for the "ring" seal repair kit.
88G8689 is the kit for GMC171 and GMC172.

The very early Mini had a brake master with .75" bore size. It used a cup on one end of the plunger and a seal on the shaft. not very common so the method to be sure is to measure the bore size before ordering. All complete replacement master cylinders are .70 bore.