I believe this is a Morgan design problem, one way or the other.
When I took mine to Berrybrook for its' first service and complained about the handbrake, they said they could do nothing further, but they offered Tims suggestion about applying the footbrake first, then on with the handbrake, which in fairness, does seem to work, though I have yet to try it on a hill, but I will.
BTW for those who don't know, there is only one pad on Morgans setup and this works footbrake and handbrake, probably from a Ford Sierra or Sierra Cosworth.
I have some rust on the inside area of the discs, which indicates that the pads just aren't gripping, even using the footbrake in the normal way, but as they bed in it will probably get better.
Discs can be made to work, and work well, especially with a short cable run, as we have in Morgans. Maybe more leverage is required, I don't know?