Morris Minor Owners Club

DJ
This might indicate a very bad earth problem at the headlights. I can only think that the high beam warning light has some sort of backfeed for it to light all the time as this earths seperatly at the speedo.
Are the headlights not working at all or is there some sort of glow ?
It might be worth hooking up a wire direct from the headlight earths direct to the earth terminal on the battery to try this first.

Have you got fibre glass front wings by any chance??
Certainly sounds like an earth problem since you say that
power is reaching the bulbs. Either that or you have blown
all of them at the same time!! If your dipper switch was
faulty then you would not get power to ALL of the headlight
bulbs....only to either dipped or main beam. The main beam
indicator being on all the time would suggest that the dipper
is stuck in main beam mode.