Partly because some of it affects us, especially with regard to foreign policy. I think there is a respect for President Obama, and also that many people, even Conservative voters, find the stupidity and extremism of the Bushes and Palins a bit too much, and find it quite hard to understand how these nutters get elected - not that Cameron is anything to write home about, but at least he's not nearly as insane as someone like Palin or Santorum. Also, we are aware that money plays a bit too much of a role in American politics; we are just beginning to find out how much of a role it plays in British politics!
Having said all that - in the last few years, there has been a rather unhealthy tendency for some elements on the Right to identify a bit too much with Republicans. E.g. the Daily Telegraph writers have become obsessed with hating President Obama and the Democrats; and the Tory 'grassroots' website, ConservativeHome, has started a sister website, 'ConservativeHomeUSA', which supports the Republicans. The British Tory politician Daniel Hannan organized a 'Brighton Tea Party' , though I'm happy to say that it was poorly attended. This sort of thing never used to be the case: Tories were generally simply pro-American, whoever the president was, and there was no attempt to amalgamate the British and American parties. There is a recently-founded British Christian Right organization, Christian Concern for Our Nation, which has links to the American organization, Alliance Defense Fund; and, at the extremes, it's said that there are some links between the Tea Party and the English Defense League.