I have reviewed the posts on this page of this thread and have the following comments.
1. I find the Connaughts narrow. The right shoe required 2 stretchings to make it wearable, but once so, my pair is very comfortable.
2. I do not have any C&J on the 337, but I am a 9 in my Westfields and a 9 in the Portman 3. My Connaughts are a U.S. 10D, bought at Barneys. Whether these are simply a UK 9E marked as a 10D or not is an open question to me, as I have heard competing responses.
3. I am a UK 9.5F on the AS 109 last; I have one, the Stiles.
4. My local cobbler let me try on a pair of Consuls he had in a UK 9.5F and they fit me.
So, to sum up, I am a UK 9E in C&J; UK 9.5F in Church's and a UK 9.5F in AS.
My right foot is larger (wider - and visually so) than my left and I have a very high arch and a very high instep on both feet.
I find the 236 last to be narrow and I would not buy shoes in that last again. I find the 240 C&J last (which now seems to be in use exclusively for BB and BS) to be exceedingly comfortable and NOT narrower overall. I have the Peal monk and the wholecut in the 240.