The building of the gazebo is a take off of the barn-building scene from Witness (1985). Even the music is a parody of the Maurice Jarre score.
When Lance and Andy approach Paul ("Simon") and Phillip ("Garfunkel") at the White Horse to enlist their cooperation, Phillip taunts, "Look who's come crawling back." This echoes the real Paul Simon's fairly infamous jab at the real Art Garfunkel ("So, Artie, you've come crawling back") on camera when Simon hosted the very second episode of "Saturday Night Live" in Oct. 1975, having persuaded Garfunkel to join him for one of the few occasions (SNL certainly being the most-watched) the duo would then be appearing together after their acrimonious professional split five years earlier.
Second time that real life mother and daughter, Diana Rigg (Veronica) and Rachael Stirling (Becky), have played Mother and Daughter. The previous was in Doctor Who's "The Crimson Horror (2013)".
The characters known as Simon & Garfunkel are actually called Peters (Paul Casar) & Lee (Simon Farnaby) in the series, the joke being that Peters and Lee were a successful British pop and folk duo in the 1970s and near contemporaries of Simon and Garfunkel.
Toby Jones (Lance), Mackenzie Crook (Andy) and Simon Farnaby (Art) also appeared in Christopher Robin (2018) together as Owl, Newspaper seller & Taxi driver respectively.