Common modification/upgrade to a lot of Morris Minors still running in Australia is to fit the A series Datsun motor, in 1200, 1400 or 1500cc capacities, plus fitting the 5 speed gearbox,(though quite rare here). Motors are 8 port alloy head, indestructible bottom end, cheap for parts and produce much better power and super reliable. I had a 1400 version in my Datsun Sunny wagon that had around 250,000 km on it and still ran like a Swiss watch. The motor is very similar to the Morris as Datsun had a licence to build the Morris A series motors in the late 50's-early 60's. Unlike the British Motor industry Datsun made improvements and developed the motor over the years. Another good point is all the Datsun A series motors were originally built for unleaded petrol, as 80% went to the US market. If you found a Morris with a dead motor I'd definitely recommend this way if your aren't too worried about originality.
Cheers Stephen