Begrudges housing costs around London area (7)

I believe the answer is:

resents

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'begrudges housing' is the definition.
'resents' can be an answer for 'begrudges' ('resent' can be a synonym of 'begrudge'). I am not sure about the 'housing' bit.

'costs around london area' is the wordplay.
'costs' becomes 'rents' (rent is a kind of cost).
'around' is an insertion indicator.
'london area' becomes 'SE' (South East postcode).
'rents' enclosing 'se' is 'RESENTS'.

Can you help me to learn more?

(Other definitions for resents that I've seen before include "Takes offence" , "Begrudges" , "grudges" .)

I've seen this clue in The Times.

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