Do they mean costly trouble for British capital? (5)

I believe the answer is:

bills

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'do they mean costly trouble' is the definition.
The definition suggests an adverb but the answer is not.

'british capital?' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'capital?' becomes 'ills' (I can't justify this - if you can you should believe this answer much more).
'b'+'ills'='BILLS'

'for' is the link.

Can you help me to learn more?

(Other definitions for bills that I've seen before include "Invoices" , "Draft laws" , "Beaks" .)

I've seen this clue in the Evening Standard.

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