This may just be a good story, but I think it comes from a time before divorce laws were reformed.
The "other party" often had to be "hired-in" to prove adultery. The distinctive two-tone shoes, left outside the hotel room, were easily remembered for court evidence purposes.
The builder - "In England, where a husband brings a suit against his wife charging her with adultery, the alleged adulterer must, as a rule, be made a party to the petition as a co-respondent. If the adultery is proved, the court may order him to pay damages to the husband."
So it kind of ties in with your story and that of cads and bounders. What larks.