According to the Bill Young BN1 wiring diagram in the January 2019 Healey Marque, power for the OD comes from the fused side (terminal A4) of the 35-amp fuse (This is different than later Healeys). The 50-amp fuse should only go to the horns. The supply side wire to the fuses should be brown (terminals A1 & A3); the fused wire to the horns should be brown with a green stripe (terminal A2). The fused side wires from the 35-amp fuse should all be green (terminal A4).
You could have a connection between terminals A4 and A2, causing power to the OD to go through both fuses. Check the fuse block for this. With a short in the OD circuit, the current is enough to blow both fuses, probably the 35-amp one first, then the 50-amp one.
The next problem could be the OD solenoid or a wire in the OD circuit shorted to ground (earth). Anyone know the inrush current of the OD solenoid?