Possible Clues:

• A position as inspector? Fat chance of that!
• Fatty, of animal fat
• Of animal, fat, fatty
• Fat chance of getting an inspector confused over the position
• Fat chance of this being the position at the beginning of this era!
• Fat chance of getting the position of an inspector
• Piece of publicity I come to with an attitude possibly Falstaffian
• Might the soap die with so much fat?
• Fatty having swim round in choppy sea
• Such fatty tissue made OAPs die