My knowledge of the nuances of British English come from reading authors such as P.D.James, but I have the impression that Dr. Smith is a less eminent medical doctor than Mr. Smith. Was this so, and if so, it is still the case? When does it take for Dr. Smith to become Mr. Smith? And, if the eminent medical doctor is a woman, is she referred to as Mrs. Smith whether or not she is married? Ms. Smith or Miss Smith seems unlikely, but, as I say, I don't understand the nuances. (Sorry not to have a specific quote.)
Surgeons are addressed as Mr because originally Doctors of Medicine (physicians) were university educated - unfortunately in astrology, theology and other slightly less than useful diagnostic techniques - while surgeons were merely barbers with a sharp knife and a strong stomach.
Then as surgery became more medical and respectable the surgeons kept the "mr" as a mild rebuke to the physicians.