I have a few dates for Rex noted from back issues of Gramophone. I've got 9169 down as being reviewed in January 1938, so it seems quite likely that this is from 1937.
Just added this and used 1937 as date as per the other Rex we have.
Wikipedia, and thus much of the internet, claim Horsey, Horsey was written in 1938, but I'm sticking to 1937.
Billy Cotton's earliest record here thus far?