For standard Mini disk brakes, standard master cylinders are fine.
Because the braking effort achieved for a given line pressure is
slightly higher than for front drum brakes, the rear wheel cylinders
must be slightly smaller (same pressure, less area, less force), 5/8"
instead of 3/4". The effective difference is 5x5/6x6 = 70%.

It sounds like what is happening is that the metro twin pots have even
more piston area than a standard Mini disk, so they require more fluid
to move them a given distance (but provide more braking effort for a
given line pressure).

If this is correct, then you will need a master cylinder with a larger
bore to displace more fluid, but increase the pedal effort for a given
line pressure.

I can think of two ways to check this.

First of all, what is the diameter of each of the pistons in the twin
pot calipers? What is the diameter of the pistons in a standard CooperS
7.5" caliper or a 8.4" caliper? From these you can calculate the
difference in fluid displacement required, as well as the difference in
braking efforts/effects.

Alteratively, if you don't have all the numbers to hand, if, (BUT ONLY
IF) you have the correct 5/8" rear cylinders in the car, try braking
hard to lock up the brakes. If, as I suspect, the piston area of the
twin pot calipers is significantly larger than that of standard
calipers, your rear wheels should lock up well before your fronts (and
there's another problem to fix too, btw).

The brake limiting valve may interfere with this happening, but if the
rears do lock up and they do have the right cylinders, then you
definitely need a larger bore master cylinder. If they don't, well you
can't be sure.....

I would think there must be people who have done all this before with
these types of calipers and who already know all the answers to this
problem. It may be easier to find one of them and ask them, which is
obviously what you were trying to do by asking here. It's also why I
waited to see if anyone who actually KNEW the answers would pipe up
before I answered.

What is the cylinder bore of the later type master cylinder?
What is the cylinder bore of the standard master cylinder?

(I don't have a British Mini manual handy)

If you can tell me the piston sizes for each caliper and the bore
diameter for any master cylinders you can get hold of, I can calculate
which one would best suit your purposes, but I strongly expect that the
twin pot calipers will have much more piston area and basically require
the master cylinder with the biggest bore. I also expect you'll have to
do something to fix the rear brake balance too, before you go under a
truck backwards.

Graham in Oz.