Minor example of House to put behind British Prime Minister (6)
I believe the answer is:
bhutto
'behind british prime minister' is the definition.
The definition suggests a singular noun which matches the answer.
'minor example of house to' is the wordplay.
'minor example of' becomes 'b' (I can't justify this - if you can you should believe this answer much more).
'house' becomes 'hut' (I have seen 'Small house ' mean 'hut' so perhaps 'house' could also mean 'hut').
'b'+'hut'+'to'='BHUTTO'
'put' acts as a link.
Can you help me to learn more?
(Another definition for bhutto that I've seen is " Benazir --, PM of Pakistan".)