In Britain the PM is chosen by the party in power so you don't get the divided government situations you see in the US where usually the Democrats control some of (1) the Presidency, (2) the Senate, (3) the House of Representatives and the Republicans control others. Considering the veto power of the President and the filibuster rule in the Senate that can be a formula for gridlock.
Margaret Thatcher and Ronald Reagan both represented a move to the right but when Thatcher was in power she had no effective opposition while any legislation that passed in the 1980s was a compromise between Reagan in the US and Tip O'Neill and I think between having a good conservative and a good liberal, we got a lot of good legislation in the 1980s (we got a new Clean Air Act in that time frame, for instance.)
As a result there was a lot of resentment towards Thatcher from Labor advocates who felt completely shut out, so some sang "Ding Dong the Wicked Witch is Dead" when Thatcher died
https://theconversation.com/burying-thatcher-why-celebrating...