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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
I'm thinking it needs either 25mm or 27mm tubs, but I can't find any information on what these earlier bikes used - either what size or whether they were black, tanwall or white. Any ideas?