Day I tell off student in Cambridgeshire city on purpose (12)

I believe the answer is:

deliberately

I'm a little stuck... Click here to teach me more about this clue!

'on purpose' is the definition.
(synonyms)

'day i tell off student in cambridgeshire city' is the wordplay.
'day' becomes 'd' (abbreviation for day).
'tell off' becomes 'berate' (I am not sure about this - if you are sure you should believe this answer much more).
'student' becomes 'l' (as in L-plates for learner drivers).
'in' is an insertion indicator.
'cambridgeshire city' becomes 'ely' (Ely is a city in Cambridgeshire).
'i'+'berate'+'l'='iberatel'
'iberatel' placed inside 'ely' is 'eliberately'.
'd'+'eliberately'='DELIBERATELY'

Can you help me to learn more?

(Other definitions for deliberately that I've seen before include "as intended" , "On purpose" , "Consciously and intentionally" .)

I've seen this clue in The Telegraph.

Want a hint initially instead of a full solution? Install my app