Scrub fork clean for a bit of breakfast (9)

I believe the answer is:

cornflake

'a bit of breakfast' is the definition.
(cornflakes is a breakfast cereal)

'scrub fork clean' is the wordplay.
'scrub' is an anagram indicator (I've seen 'scrubbed' mean this).
'fork'+'clean'='forkclean'
'forkclean' is an anagram of 'CORNFLAKE'.

'for' acts as a link.

I've seen this clue in The Times.

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