We did some more to the mini today.
Douglas replaced the battery cable yesterday, & we tracked down the bad earth ( it turns out that Hammerite is a particularly good insulator)
Today we rebuilt the fuel pump with new internals ( & bench tested it) & replaced needle & jet in the carb.
After refitting everything, we still weren't getting fuel to the engine from the tank. Out came the tank, which had rusty sludge blocking the outlet.
Once that was fixed we had fuel to the carb !
The car then started second crank, and now moves under its own motive power !