After staring at the bare steel for a while longer I spotted a similar pattern on the seat tube:
Perhaps you can see the same headbadge outline a little below the center of the photo; and above it, a clean rectangle exactly the size of a Reynolds 531 decal.
There were also stains on the down tube. I took lots of photos, such as this one:
Again you can see that there's a pattern of clean shiny steel, surrounded by a stained steel. What the pattern is, however... well, that's not very obvious. I assumed, of course, that it was writing; but the orientation was wrong for that. If it said "FOTHERGILL" on the right side of the frame, the F would be down toward the bottom bracket, and the LL's up by the headset; and on the left side of the frame the F would be up near the headset and the LL's down at the other end. But on my frame, the pattern was oriented the same way on both sides; fatter toward the headset, narrower at the other end. The photo shows the narrow end.
So I drew it. I also asked my daughter, who was about 11 years of age at the time, to draw it. She had no preconceived notion of what she was looking at, so I trusted her eye. We came up with basically the same thing. I can't lead you through every stage of my thought process, but I eventually realized that, like the head badge, the design was a triangle with something over it; and I eventually came up with this:
I later realized that there was a period after the J. I did not know about this thread and did not know that my headbadge was probably the earlier version that doesn't have the bicyclist in it. Satisfied that I had learned all I could learn, I painted my frame (enamel, brushed on, carefully sanded between coats...) made my own decals, and ended up with this....
27" wheels, Sturmey Archer 5 speed hub (note the bar end shifter and the trigger shifter); Williams 1200 chainset; GB Hiduminium brakes; Soma "Lauterwasser" handlebar; and so on.
To be continued....