One certainly can't deny Margaret Thatcher's historical importance. She was a rarity among politicians, among public figures in general, that she transcended her arena and became a general icon of popular culture, the way Ali transcended boxing. Not many politicians do that: In America in my adult lifetime, Reagan, the Clintons, Obama. That's about it. Maybe Cheney, but in a bad way. But Thatcher was such that an impersonator could show up in a Bond film (For Your Eyes Only) or even on an America-only sitcom, and everyone knew who it was and what she represented.
The thing that made her a hero to the right was undoubtedly the way she took on and beat Arthur Scargill and the unions. Here's a very good BBC piece from 2004 on how that happened. What has happened with Scargill, by the way? Well, I (and I'd guess most American readers) didn't know this, but he's still at it. He helped form the Socialist Labour Party in 1996 after New Labour ditched the platform clause committed to nationalization of industry. But matters haven't exactly gone Scargill's way. Britain went from 13.5 million union members to around 6 million today.
Of course, the Reagan-Thatcher relationship was much lionized on both sides of the drink. It was indeed a very lucky thing for conservatism in both nations that at the exact point in both nations' histories when the general public was ready to break with liberalism, the conservative parties just so happened to offer leaders whose personalities were large and strong and appealing to many people and were very nicely in tune with the times in both countries. Reagan had that American optimism, Thatcher was a bit more somber. But they were more similar than different.
We learned recently that they did have their disagreements--with Thatcher standing to Reagan's right! Reagan urged her to cut a deal on the Falklands, papers released by the British government last year urged, but she said no. The New York Times:
“The best chance for peace was before complete Argentine humiliation,” the memo recorded Reagan as saying. “As the U.K. now had the upper hand, it should strike a deal now,” rather than act in a way that further hardened Argentine feelings.
But the memo said Mrs. Thatcher rejected the president’s appeal for talks three times, becoming more emphatic each time. “Britain had not lost precious lives in battle and sent an enormous task force to hand over the queen’s islands to a contact group,” Mrs. Thatcher told him, adding a brusque reminder that Britain had been forced to “act alone, with no outside help,” in recovering the islands, an oblique reference to the American refusal to be drawn directly into the conflict on the British side.
The other difference between Thatcher and Reagan is that the Tories haven't gone mad and made Thatcher look like a milquetoast moderate. In this sense her legacy has been more durable than Reagan's. She re-centered British politics to a place where it's more or less stayed, while today's American right has completely left Reagan in the dust.