Popular breakfast show on the radio (6)
I believe the answer is:
cereal
'popular breakfast' is the definition.
'cereal' can be an answer for 'breakfast' (I've seen this before). I'm not sure about the 'popular' bit.
'show on the radio' is the wordplay.
'show' becomes 'serial' (serial is a kind of show).
'on the radio' shows a homophone (sound like).
'serial' is a homophone of 'CEREAL'.
Can you help me to learn more?
(Other definitions for cereal that I've seen before include "Grass cultivated for food" , "Grain crop" , "Eg, wheat, rice" , "'Wheat or maize, say (6)'" , "Food prepared from grain" .)