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."
"Moscow Rules" and "London Rules" are fictitious, the second made up by Mick Herron (on whose book of that title the series is based) as counterpoint to the first, made up by John L Carré.
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.