You're right, most members of the British Conservative party would be Democrats in the USA. Personally, I'd describe myself as a Libertarian, which puts me far to the right of the British Conservative party and similar to American Libertarian Conservatives. As for the BNP, I hate their guts, they are totalitarian national socialists.
The political environment has still not arrived for the libertarian movement in Britain to set up a political party, although the subject is being broached. Unfortunately, the British political psyche is essentially statist, due to our history, and the fact that much of our media are leftists (most notably the BBC). They would paint a fledgling British Libertarian party's stances as reckless, immoral and/or dangerous to law and order etc. I wish we could set up a British Libertarian party to get the ball rolling now, but until the BBC et al. are discredited, such a party wouldn't stand a chance at the polls.
which makes them nationalistic collectivists, which makes them militant Leftists.
One of the biggest scams the Left has been able to pull off was the redefinition of fascism as "a far-right-wing dictatorial form of government" despite the obvious facts to the contrary.