Oblivious to the world, like flipping British PM (6)
I believe the answer is:
asleep
'oblivious' is the definition.
(thesaurus)
'like flipping british pm' is the wordplay.
'like' becomes 'as'.
'flipping' shows that the letters should be reversed in order.
'british pm' becomes 'peel' (19th-century prime minister Robert Peel. I am not sure about the 'british' bit.).
'peel' in reverse letter order is 'leep'.
'as'+'leep'='ASLEEP'
'to the world' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for asleep that I've seen before include "Inattentive; numbed" , "Slumbering" , "coiled up?" , "Resting unconscious" , "Having nodded off" .)