In the books Jackson Lamb is said to resemble Gary Oldman's Remembrance (1982) co-star Timothy Spall "gone to seed" and "with worse teeth."
"London Rules", in addition to being the title of the fifth book of the series, is a play on "Moscow Rules," a set of unofficial rules for operating in Moscow developed by the CIA and later written down by Tony Mendez that John le Carré mentions in the source novel for Gary Oldman's movie O Espião Que Sabia Demais (2011) and
Deep in the credits under "Camera Trainees" can be seen Alfie Oldman, Gary Oldman's son. He's worked on several movies that Gary starred in.
References to animals feature heavily throughout the show. "Slow Horses" is the name given to the misfit and exiled agents sent to Slough House. "Dogs" are the MI5's internal security and investigation unit, seen as the muscle who police the MI5 employees. "Stoats" are watchers who perform surveillance on a target. "Tiger team" is a group that tests for weaknesses in an organisation's security measures. "Weasels" are the MI5 analysts. There is also "Lamb", "Spider", "Spooks zoo" (Berlin), "Project Cuckoo", "Flea", "Cicada", "The Kennel", and "The Beast".
In the books, the Peter Judd character is clearly based on (then) future British Prime Minister Boris Johnson. In the TV series, this connection is far less obvious.