Peter
Sorry to hear you are having problems.
My car refused to start on the river ferry in Cornwall last October, but after a panic taking the key out and trying again it started. The official dealer answer is that after 30 seconds the immobiliser kicks in so you have to take the key out and try again, absolute rubbish as it doesn't always happen. I also frequently have the engine not turnover at all but turning the ignition off and on again has sorted that so far.
Other than those minor hiccups I had exactly the same problem. Moved the car out of the garage ran perfectly, stopped it and went back to it after about two hours after my chores. Wouldn't start but did cough and splutter a bit. Left it another couple of hours, it is a Morgan after all, but whilst turning over ok and a big of a stutter nothing. Called out the breakdown service who asked me to turn the engine over and it started first time!
No issues since but no idea what the problem was.