Firstly I would consider the condition of your fuel tank. You may need to remove it, and have it treated for rust, and coated. Old age will cause this problem, although ethanol fuel may accelerate the problem.
If you fuel tank has rust issues, then you fuel lines may be clogged also. It is easy to run new ones with 1/4 in ethanol compatabile rubber hose.
Carb floats. With brass carb floats in ethanol fuel, replacing them is almost part of the de winterisation process, as they sink after a time in ethanol fuel. Replace them with stay up floats form Burlen UK, or from British Parts Northwest. Also consider replacing you seats while you are at it.
I have not heard of any problems or experienced problems with the diaphragm in the fuel pump.
James.