Luddite, wen starting a non EFI Morgan the starting circuit energisers the fuel pump so you do get fuel pumped to the carburettors, on releasing the ignition switch when running it switches to the oil pressure switch which is somewhat similar to the inertia switch on a EFI car in that when the engine stops the fuel pump electrical circuit is broken. There is a good article on Gomog. There have been a few failures of these oil pressure switches but in the field it can be bypassed with say a a paper clip or similar to at least get mobile again. This is very much a temporary fix.
Doug
Deep deep dowunder