The opposite. Knowing now, all I wanted someone to say was that in the UK, individual politicians are less 'essential' to the political culture there.
The real difference - from the U.S. - is in the mechanisms of election and governance. Political culture follows on from those mechanisms, i.e. you elect a party, not an individual. American elections allow for split ticket voting. British elections, to my understanding, do not (at least at the national level). The Prime Minister is "just" an MP who's been internally elected leader of the party that controls Parliament.
Granted the recent/post-Brexit greatly increased fragility of PMs and their inability to survive policy defeats that their predecessors would've been probably able to ride out is a more complicated question. Both the PM and Tory leadership seem so toxic that you wonder why people even want the job. Ambition and power, obviously, but it seems like if you're young enough you'd be better off waiting a few years and hoping for a better situation.