No proper English gentleman would end a sentence with a preposition.
The "British man" in this passage is Sir Leigh Teabing, an effete English national residing in Paris who is insistent about his nationality and his class. His manor gate sports an intercom terminal on the right-hand (UK) side of the driveway because Mr. Teabing is just that British.
Teabing, as a character, is written as one amongst the most proper and the most gentlemanly of Englishmen a knight (and not one like Jagger or McCartney,) a tradition-minded member and protector of the Order of the British Empire.
It's true that "who do you work for?" is a perfectly good English-language question for normal conversation but it's not a good British question, and it is certainly not the Queen's English. The substitution of the stuffier "whom" does not make it so, either.
The character, properly drawn, could only have asked "for whom do you work?"
That, in a page, is "The Da Vinci Code" as literature.