Possible Clues:

• Fedora lookalike
• A short brimmed hat - or a novel by George du Maurier?
• Hear about the Italian bishop's hat
• Attempt to secure one pound for a hat
• Short tweet getting through, it's felt
• Novel hat for a Parisian model
• Fedora-like hat
• English hat similar to a fedora
• Soft hat with indented crown
• Goes on ahead having three pound? Yes!