alternatehistory.com

Your challenge, should you accept it, with a PoD of the partitioning of Ireland into Northern Ireland and the Irish Free State in 1922, is to elect / appoint any politician, from any political party, into the Parliament of Northern Ireland (if before 1973), or into any of the successive Northern Ireland Assembies (if after), then (with any number of required intervening steps) into the office of Prime Minister of the United Kingdom.

If this is too difficult, the challenge may also be fulfilled simply by the individual in question being born and raised in Northern Ireland and having held some position of political power there prior to becoming the British PM.
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