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That's brilliant - thanks for the links. So it looks like sizes were between 1" and 1-1/4".
I've come across a bit of a problem with my repaint. The Halfords paint I'm using is reacting with traces of whatever is left on the fork. I managed to get the fork to what looked like completely free of the old paint but it is still reacting in places. I won't be able to get the frame anywhere near as clean because of the nooks and crannies. I think I'm going to strip off the paint I've put on the fork and switch to enamel, which I know won't react. It'll also give a better finish than Halfords black which is crap.
have a look through the 1939 Brown Bros catalogue. Start from this page
https://www.flickr.com/photos/22983673@N02/14656343932/in/album-72157645280907377/
and page 72 of the 1939 Aids
http://veterancycleclublibrary.org.uk/ncl/pics/Holdsworth%20Aids%20catalogue%201939%20(V-CC%20Library).pdf
and the 1938 Constrictor catalogue
http://veterancycleclublibrary.org.uk/ncl/pics/Constrictor%20catalogue%201938%20(V-CC%20Library).pdf