There are some things we could learn from the UK. For example, I like their “question time” when the Prime Minister has to stand before Parliament and take questions directly. How’d you like to see Obama have to do that? (Assuming there were any GOP reps or senators with the guts to ask tough questions).
However, for the most part, Britain’s “Conservative Party” is like the RINO wing of the GOP. If you want to emulate a British political party, better to emulate UKIP, the United Kingdom Independence Party.
The PM is a bit more like our Speaker of the House, or maybe House Majority Leader. A PM is a voting member of the legislature and does not represent a different branch of government. The PM must remain in the good graces of his party, or else he can be removed in a few hours. No need to wait for a general election. He wouldn’t face the music unless he had to!