North American MGBs with the ignition relay i.e. 77 and later rely on a functioning anti-runon system to shut down the engine by starving it of fuel, as a wiring design error (1977 and some 1978 North American models) results in voltage still being supplied to the ignition system when the ignition has been turned off. Any defects in the operation of the valve or pretty-well anywhere in the emissions plumbing (blockages or leaks) can cause this to happen. UK cars don't suffer from it as they never had the anti-runon system, the wiring error was discovered immediately and corrected (but only on those cars).

The factory cure was to move the feed to the ignition system from the output of the ignition relay (i.e. its contact) to its winding, *and* to move the feed to the ignition warning light from the relay winding to its contact, i.e. swap the two wires over. In theory either change should have solved the problem. In practice it's much easier to move the ignition feed wire as that is only a matter of a couple of inches - once you have identified which wire feeds the ballast resistance and coil.

Thanks to Paul Hunt for this information.