The auto shutoff on gas filler nozzles depend on a venturi in the gas flow path and a sensing line that ends just inside the end of the nozzle. The venturi creates a bit of a vacuum as the gas flows through it and it causes a small stream of air to be sucked up the sensing line. As long as the fuel doesn't reach the end of the sense line a diaphram controlled shutoff valve allows the gas to flow. As soon as the nozzle tip is immersed in the rising gasoline the diaphram valve cuts off the gas flow due to the change in pressure in the sense line due to it pulling gas instead of air.
If that system doesn't work for your Healey it can only be because the fuel level rises in the filler neck and the nozzle is at such an angle or position that the sense line tip isn't being immersed. I'll bet if you carefully fill the tank and slow down, maybe way down, before the fuel rises into the narrow neck of the tank, that the shut off will work. Also, if you look into the tip of the nozzle and see where the sense line is you may be able to better position it so it sees gas earlier as it rises in the filler neck. Even knowing this and trying to make it work I put a towel around the base of my filler because it is in the boot (BN2) and I dont like gas seeping around.