This site gives history of Chrysler/Plymouth/Dodge exports to the UK (apparently built in US and Canada as right-hand drive), but unfortunately no pictures from the 1930s:
https://www.allpar.com/world/england.html
Edit: on re-reading, it's not clear to me if only stampings/parts were exported at that time and then assembled as right-hand drive in the UK. Farther down the page, it seems more clear that this was done in the 60s.