I would use the extra comma, based on this guidance found in the Purdue OWL:
Use commas after introductory a) clauses, b) phrases, or c) words that come before the main clause.
So, for the purposes of determining whether or not there should be a comma, let's rephrase your sentence:
When cholera did break out in Britain, something happened.
As the Purdue OWL goes on to say, “introductory clauses are dependent clauses that provide background information or "set the stage" for the main part of the sentence, the independent clause.” In this case, the main phrase is the part we just shortened to “something happened”:
Farr believed that it was caused by miasma.
I would follow the OWL's guidance, and put a comma at the end of the introductory clause that starts your sentence.