Minor example of House and The Observer initially supporting British PM once (6)

'minor example of house and' is the definition.
I can't tell whether this defines the answer.

'observer initially supporting british pm once' is the wordplay.
'initially' says to take the initial letters.
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'pm once' becomes 'hutt' (I am not sure about this - if you are sure you should believe this answer much more).
The initial letter of 'observer' is 'o'.
'b'+'hutt'='bhutt'
'o' after 'bhutt' is 'BHUTTO'.

'the' is the link.

Can you help me to learn more?