What U.S. political party is the U.K. Conservative Party most similar to?

I am an American and I would be a die-hard Republican if it were not for the religious lunatics and rednecks that have taken over the party and George W. Bush- now everyone across the globe thinks that the Republican Party stands for mental retardation. I like Obama quite a bit, but if he ran against Rudy Giuliani for the presidency in 2012, for example, my vote would go to Giuliani. I do know quite a bit about what the Conservative Party stands for and I know I would easily be a member of the Conservative Party if I were a British citizen, but what confuses me is there is Margaret Thatcher, whom was viewed as being extremely conservative, almost to the point of being to the right in the political spectrum of Attila the Hun and close to Reagan, and now there is David Cameron and Boris Johnson, both of whom publicly endorsed Obama for the 2008 presidential election. Is the Conservative Party moving to the left, or has it always been closer to the Democratic Party than Republican Party?