"The real thing about Margaret Thatcher is that she didn't just lead our country. She saved our country," Cameron said, "and I believe she'll go down as the greatest British peacetime prime minister."
In Washington, President Obama said many Americans "will never forget her standing shoulder to shoulder with President [Ronald] Reagan, reminding the world that we are not simply carried along by the currents of history. We can shape them with moral conviction, unyielding courage and iron will."
And former first lady Nancy Reagan said her husband and Thatcher "enjoyed a very special relationship" driven by a common hatred of communism. "Ronnie and Margaret were political soul mates," she said.
In Poland, Foreign Minister Radoslaw Sikorski said his country should erect a statue of Thatcher. In a tweet he praised her as "a fearless champion of liberty, stood up for captive nations, helped free world win the Cold War."
Not all Britons were upset. Several hundred people gathered in Glasgow and in London's Brixton neighborhood for impromptu celebrations, complete with party hats and streamers.
The National Union of Miners - which tussled with Thatcher in a long 1984-85 strike, and lost - expressed condolences to Thatcher's family, but said: "The damage caused by her fatally flawed politics sadly lingers on. Good riddance."
Harsh criticism came from Northern Ireland and Argentina, where Thatcher's reputation for unbending determination received early tests - when breaking an Irish Republican Army prison hunger strike in 1981 that left 10 inmates dead, then leading Britain into a 1982 war to reclaim the Falkland Islands from Argentine invaders.
"She was presented as the Iron Lady, but she was open to change and she did change," said Noel Dorr, one of Ireland's senior diplomats in the 1980s who had close personal dealings with Thatcher.