Possible Clues:

• GK Chesterton's detective
• The hero of stories by G.K. Chesterton
• Solver adjusted the bra, wearing anxious look
• Female's apprehended by overweight British private detective
• G.K. Chesterton's detective character
• Chesterton character
• Detective's worried look when accepting a task initially simple?
• The Innocence of - - - - , (GK Chesterton)
• Sleuth is overweight, the female copper, maybe?
• "The Invisible Man" sleuth