Never had an issue with any of the handbrakes on my Morgans.
Make sure the ratchet quadrant is in good condition, touch up the teeth with a triangular file or replace, also check the plunger in the handbrake lever, sometimes these stick either due to rust or old hardened grease.
The handbrake cable should be kept well lubricated and checked for fraying. Cable also needs to be routed correctly. A small spring between the adjuster and the pivot also increases efficiency.
On the 7HA axle at least, the pivot on the axle could do with a little lubrication as do the rod ends. Check the rod ends for wear as well, a little bit of wear on all four adds up to a fair bit of lost travel!
Hope this helps
Arwyn