This focuses some on a young man who thinks he's a wizard. Mark Williams (Father Brown) and Adrian Rawlins (Dr. Henshaw) both acted as fathers of wizards in the Harry Potter universe. Adrian portrayed James Potter who was Harry Potter's dad and Mark Williams portrayed Arthur Weasley who was Ron Weasley's father.
The bible verse that Father Brown references in the end to Sarah (Matthew 9:22) reads, "Jesus turned, and seeing her he said, 'Take heart, daughter; your faith has made you well.' And instantly the woman was made well." (from revised standard version)
Mrs Underwood has the same distinct green tea set with a bright green band, as Father Brown.