Dreadful rain over British Island's capital city (7)
I believe the answer is:
nairobi
'capital city' is the definition.
(capital of Kenya)
'dreadful rain over british island's' is the wordplay.
'dreadful' indicates an anagram.
'over' becomes 'o' (cricket abbreviation).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'island' becomes 'i' (geographical abbreviation).
'rain' is an anagram of 'nair'.
'nair'+'o'+'b'+'i'='NAIROBI'
(Other definitions for nairobi that I've seen before include "Kenyan capital" , "Robinia strangely found in Kenya" , "Foreign capital" , "Flat round object" , "I, a robin (anag) - city" .)