The poem that Father brown reads from the book is Antigonish, an 1899 poem by the American educator and poet, William Hughes Mearns. It was inspired by reports of a ghost of a man roaming the stairs of a haunted house, in Antigonish, Nova Scotia, Canada. The poem was originally part of a play called The Psyco-ed, which Mearns had written for an English class at Harvard University.
The building used for the health spa had previously been used as the set in S1 E10 of Shakespeare & Hathaway: Private Investigators (2018), Ill Met by Moonlight (2018).