A Taoiseach is effectively a Prime Minister. Constitution of Ireland says... :"The head of the Government, or Prime Minister, shall be called, and is in this Constitution referred to as, the Taoiseach."
Unlike the US and needing to be born in the US to be president, no equivalent rule applies to be PM of the UK.
Quite common for it to be referred to as British PM even if not entirely correct.
Today's Irish TImes for example...
http://www.irishtimes.com/news/politics/taoiseach-and-british-prime-minister-pay-respects-to-war-dead-in-flanders-1.1633597
Seemingly not you though.