When Andy and Becky arrive at the cottage and Andy describes all the work he's going to do on the old house, he refers to fixing the shingles, fixing the door, and oiling the hinges - all lyrics from This Old House, written by Stuart Hamblen in 1954 and covered by many artists including Rosemary Clooney and Shakin' Stevens.
When Andy and Becky are driving to the cottage and imagining what it might be like, Andy responds to Becky's comment that he is a dreamer by saying, "You may say that I'm a dreamer, but I'm not the only one ..", the lyrics to John Lennon's song Imagine. This is one of a few instances when Andy quotes song lyrics in his conversations with others.
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)".
Toby Jones (Lance), Mackenzie Crook (Andy) and Simon Farnaby (Art) also appeared in Christopher Robin (2018) together as Owl, Newspaper seller & Taxi driver respectively.
The characters known as Simon & Garfunkel are actually called Peters (Paul Casar) & Lee (Simon Farnaby) in the series.