Morris Minor Owners Club

No oil should escape from the oil pump! The cover is just that - a cover, it's not intended to seal anything. There is an open drain hole just below the pump - obviously if there is highish crankcase pressure - fume etc will be blown up through there, and can escape around the 'cover'. No oil should leak when the engine is not running - unless the sump is perforated or cracked! The most likely leak source is the rear crankshaft oil 'seal' which is not a seal at all - it's just a labyrinth scroll - and if the crankcase pressure is high - it can't keep the oil in! Other more simple possibility is faulty cork seals at the ends of the sump - easy enough to drop the sump and renew them.

I am just guessing about the oil pump - I was just trying to think what would cause the car to leak oil, but only on the move.

Hopefully it won't be an engine out job

Pressure in the crankcase forces oil out anywhere - but especially at the rear seal. Take the oil filler cap off when the engine is running - plume of smoke/fume tells the sorry tale.