Bill B wrote:
Adding to the John Smidt quote, there was no need to alter any ID plate or stamped number on a car because your annual NSW registration certificate did not contain the VIN/Chassis No. or body No. The only form of identifying a vehicle was the engine number on the rego papers until some time around 1994 and it was straightforward to legitimately register the new engine number if a motor was swapped.
Also, the rego papers did not indicate that the car was a Cooper S - just "Morris Sedan".
So it was all very easy to do.
To add to what Bill has said, engine reconditioners and engine swaps were plentiful and common (not so much with another type of car necessarily as it means these days but a good used engine from a wreckers or a rebuild)...
Having said that, hot rodding was also common...like the early Simca Aronde with a stove hot grey six that lived near me...Morris Minor Ute with hotted up Cortina driveline etc...