The episode is set in 1953: The gravestone gives the year of death for the Haggards as 1951 and Edmund Noon states he"s been on the run for 2 years.
When the vagrant Blind 'Arry tells Mrs. McCarty and Bunty that he saw Father Brown yesterday, there is a wide shot with the headstone of George and Jasmin Haggard in the foreground. In the previous scene, Sergeant Goodfellow finds a newspaper article on Inspector Mallory's desk which tells of George and Jasmin Haggard's murder in their home at Spencer Hall in July, 1951. The partially visible police report also lists Jasmin Haggard as a murder victim.