For anyone mildly interested in the minutae of such matters.....
Cancel my previous comment about the original Lucas chrome screw being a BA thread, it is not.
The thread is UNC (course). I can't make out enough of the markings on the tap but it's UNC with a 2.8mm drill size.
What a sad life I lead!
You have checked, and I haven't, so you must be right, but I'm very surprised. 5BA is 2.7mm / 43tpi, Number 6 UNC is 2.8mm / 32 tpi, 3.5mm metric is 2.9mm / 42.3 tpi (.6mm pitch)
Quite a difference in pitch?