Donald,
I hope you like to unravel wiring harnesses. The wires that feed your headlamps are crossing over somewhere, probably with some abrasion in your harness. Was your car stored in a barn for an extended period where vermin could have chewed on your harness? Since neither the headlights nor the starter motor run throught the fuse box, I would think that the two circuits touch one another when you activate the headlights. Should be under the dash within all that spaghetti twist of a harness. Have you considered doing a rewire of you whole harness? Not that bad a job really. Contact British Wiring (britishwiring.com) for prices. This really is a weekend project, perhaps a long weekend. What's interesting is the fact that the headlight switch only gives a momentary bust to the starter, just as you would do with the keyswitch. Seems that turning on the headlights and having the car start is frightful enough that you only give it that momentary bust it needs, otherwise you would be hanging up your starter. Now, this question isn't a leadup to a really bad joke is it?
Bill