Merlin wrote:
I have two very productive quince trees, however a large proportion of
the fruit is affected by a "problem". The skin has largish numbers of
tiny black / grey dots and when you cut (hack!) the fruit open the
inside is heavily veined with brown to such an extent that 50%+ of the
fruit mass is brown and because it's veined that makes 100% of the fruit
mass useless.
Does anyone recognise this condition and can anyone put a name to it?
And ideally of course, I'd like to know what I can do to prevent it in
future.

How are the leaves and branches? Do you have black dots on the leaves
too? Or are they red? You might have Monilinia fructicolia (fruit rot).
Are the trees shadowed by a larger tree?