Combative and determined to get her way, Margaret Thatcher divided opinion down the middle in life — and in death.

Many leaders lauded Thatcher for her steely determination to modernize Britain’s industrial landscape, even at the cost of strikes and riots, and to stand beside the United States as the west triumphed in the Cold War versus the Soviet Union. Others saw a pitiless tyrant who preferred conflict to compromise.

Yet virtually all, friend and foe alike, could agree on one overarching point expressed today by British Prime Minister David Cameron: The Iron Lady, he said, was "a great Briton."

As flags at Buckingham Palace, Parliament and across the United Kingdom were lowered to half-staff, the palace said Queen Elizabeth II would send a private message of sympathy to the family of the 87-year-old conservative icon.

Government officials began preparations for a London funeral with military honors at St. Paul’s Cathedral, though no date was fixed, followed by a private cremation.

"As our first woman prime minister, Margaret Thatcher succeeded against all the odds," Cameron said in Madrid. He cut short his trip to Spain and canceled a visit to France to return to London for the funeral preparations.

"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 Barack 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."

In Poland, Foreign Minister Radoslaw Sikorski said his country should erect a statue of the British leader. In a tweet he praised Thatcher as "a fearless champion of liberty, stood up for captive nations, helped free world win the Cold War."

Former Prime Minister Tony Blair, who ousted the Conservative Party from power seven years after Thatcher’s resignation, conceded that Thatcher had been right to challenge labor union power — the traditional bedrock for Blair’s own Labour Party.

"Very few leaders get to change not only the political landscape of their country but of the world. Margaret was such a leader. Her global impact was vast," said Blair, who credited Thatcher with being "immensely supportive" despite their opposing views on many issues.

"You could not disrespect her character or her contribution to Britain’s national life," Blair said.

Discordant notes 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.

Gerry Adams, leader of the Irish nationalist Sinn Fein party that gained strength from Thatcher’s confrontation with IRA prison demands, denounced her as a hypocrite who sanctioned secret talks with senior IRA figures yet refused any concessions in public.

"Here in Ireland her espousal of old draconian, militaristic policies prolonged the war and caused great suffering. She embraced censorship, collusion and the killing of citizens by covert operations," said Adams, whose party ultimately gained a share of power in Northern Ireland after the IRA ceased fire and Blair invited Sinn Fein to the negotiating table.

Many other Irish politicians countered that Thatcher talked tough, but was more pragmatic in private — and dramatically demonstrated this by signing the Anglo-Irish Agreement of 1985 giving the Republic of Ireland a role in Northern Ireland for the first time. She struck the deal, infuriating the north’s Protestant majority, barely a year after the IRA tried to assassinate her in a hotel bombing.

"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.

Argentina’s government offered no official reaction, but scores of Argentines posted criticisms of her on Twitter, blaming her for the deaths of 649 Argentine troops during the South Atlantic conflict. Some 255 British military personnel and three Falkland Islanders also died.

Falklands lawmaker Mike Summers said Thatcher was "one of very few political leaders who could have mounted the expedition she mounted in 1982 to restore our freedom, and from a Falkland Islands perspective she will be forever remembered for that."

Britain’s pop culture icons past and present also sounded off about the woman who dominated the British political landscape through the 1980s. Many noted her inspirational role to women, even though Thatcher herself famously eschewed feminism and rarely promoted women herself.

"Thinking of our 1st Lady of girl power, Margaret Thatcher, a green grocer’s daughter who taught me anything is possible," tweeted a former member of the Spice Girls band, Geri Halliwell.