These are the shallow cone-shaped objects that the release bearing pushes on, with a steel band (disc spring) on the underside that presses against the flywheel. This provides the clamping force on the clutch plate that ultimately passes the torque/horsepower to the wheels (via the gearbox of course!). This component is therefore available with various different spring rates/tensions dependent on the application.
With the exception of the fact the two-piece flywheel is two pieces bolted together - this and the later one-piece cast item can be treated as the same thing. They will universally fit all transverse engine cranks from 1964 onwards, so that should be easy enough. If all you can get is the hulking great 1300 type, then this too is as universal to fit, but I highly recommend you get that extra cast lump machined off of the outer edge as a bare minimum.
One of the more common questions asked by Mini owners is "why doesn't my clutch disengage properly?" or "why is it hard to engage gears?" The usual symptom is that the clutch engages right at the floor and you find yourself embedding the pedal in the carpet to avoid grinding gears. Given that the clutch worked properly when the car left the factory the obvious answer is 'wear'.