Had a pork-pie reluctantly? (3,4,3)

I believe the answer is:

ate ones hat

'reluctantly?' is the definition.
I know nothing about this answer so I can't tell whether this works.

'had a pork-pie' is the wordplay.
'had' becomes 'ate' (e.g. I had an ice cream).
'a' becomes 'one'.
'pork-pie' becomes 'shat' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'ate'+'one'+'shat'='ATE ONES HAT'

I've seen this clue in The Times.

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