Cockney's semi-embarrassed — he burnt some cakes allegedly (6)
I believe the answer is:
alfred
'he burnt some cakes allegedly' is the definition.
(reference to a legend about Alfred the Great)
'cockney's semi-embarrassed' is the wordplay.
'cockney's semi' becomes 'alf' ('half' said with a cockney accent, dropping the 'H').
'embarrassed' becomes 'red' (I've seen this before).
'alf'+'red'='ALFRED'
(Other definitions for alfred that I've seen before include "... the Great, 9th-century Anglo-Saxon king" , "Former king" , "Cake-burning king" , "Saxon king" , "King after Ethelred" .)