Entropy, you know I put that there just for you. Just to rile you. You took the bait.
Ok.
They fought against religious tyranny, bringing that viewpoint wherever they went
That doesn't quite match the historical evidence in Britain. There were constant riots, lynching and such from the Reformation up until vaguely recent times, over the protestant/catholic divide. In our colonies we typically
tolerated other religions, but witchcraft and blasphemy remained crimes (still are, technically but it's like treason - we never use those laws).
As for it's influence on government thinking... that's a hard one. Certainly that influence was there, but I don't think it had much effect on our politics or economy. It affected our imperialism, as it was used (along with rascism) as justification for conquering everywhere that sat still long enough, but then it was more of an excuse. I'm inclined to believe that, on the national level, any given religion has little effect unless it is taken to fanatical fundementalist levels. The rest of the time it's just a different name.