Cook a bit of grub badly (5)

I believe the answer is:

grill

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'cook' is the definition.
(grilling is a form of cooking)

'a bit of grub badly' is the wordplay.
'a bit of grub' becomes 'gr' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'badly' becomes 'i'll' ('ill' can be adverbial as in 'ill-advised').
'gr'+'ill'='GRILL'

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(Other definitions for grill that I've seen before include "Screen" , "interrogation?" , "Broil" , "Interrogate - cook" , "rack" .)

I've seen this clue in the Evening Standard.

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