Considering the longevity of Morgans....look at the ages of cars at your next meet...there is a strong chance of sticking brakes.
Servicing by changeing pads/ shoes and fluid can be a regular but eventually cylinders and calipers will deteriorate with seals failing and piston corrosion. How many get a thorough service of strip/clean/rebuild etc?
Morgans tend to do low-ish mileage too and this can contribute to becoming sticky. I bought a Proton as a runabout for sospan jr a few years ago while he was in Uni... Low mileage and a great runner but a brake piston seized in the caliper. I bought new one and stripped the old one out of curiosity and there was noticeable corrosion of the piston.
There are good refurb companies who can strip/ rebuild and supply upgraded parts like stainless pistons etc. and if I don't do it myself then they could be in the reckoning.
One company shows their process here
www.bigred.co.uk