Bulb? – unlikely – not both of them.
Emailed my favourite source of electrical advice and asked what else it could be.
Relay, he suggested.
We checked the fuses, all fourteen of them. Then we looked at the little black box stuck on the side of the fuseboard. A three pin plug, one of which was dirty.
Scratched the dirty bits off, and put it back in. Switched on the headlights. And main beam. And back again. Working perfectly.
Shouldn’t have even bothered with the fuses. Spot-on diagnosis, and not for the first time. Top tip. Thanks pal.