David Cameron led tributes to South Africa's first black president Nelson Mandela, saying "a great light has gone out in the world".
The flag at No 10 will be flown at half-mast in honour of the former leader, who was a "hero of our time", the Prime Minister said.
Cameron said: "A great light has gone out in the world. Nelson Mandela was a towering figure in our time; a legend in life and now in death - a true global hero. Across the country he loved they will be mourning a man who was the embodiment of grace.
"Meeting him was one of the great honours of my life. My heart goes out to his family - and to all in South Africa and around the world whose lives were changed through his courage."
MPs will be given the opportunity to pay tributes to Mr Mandela in the House of Commons on Monday, he added.
Labour leader Ed Miliband called his work to unite South Africa in the face of personal hardship and oppression "extraordinary".
He said: "The world has lost the inspirational figure of our age. Nelson Mandela taught people across the globe the true meaning of courage, strength, hope and reconciliation.
"From campaigner to prisoner to president to global hero, Nelson Mandela will always be remembered for his dignity, integrity and his values of equality and justice.
"He was an activist who became president and a president who always remained an activist. Right to the end of his life he reminded the richest nations of the world of their responsibilities to the poorest.
"Above all, he showed us the power of people, in the cause of justice, to overcome the mightiest obstacles. He moved the world and the world will miss him deeply.
"During the struggle against apartheid, the Labour Party was proud to stand with the people of South Africa in solidarity. Today we stand with the people of South Africa in mourning."
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Former prime minister Tony Blair said the political leader was a "great man" who had made racism "not just immoral but stupid".
"He was a unique political figure at a unique moment in history," he said.
"Through his leadership, he guided the world into a new era of politics in which black and white, developing and developed, north and south, despite all the huge differences in wealth and opportunity, stood for the first time together on equal terms.
"Through his dignity, grace and the quality of his forgiveness, he made racism everywhere not just immoral but stupid; something not only to be disagreed with, but to be despised. In its place he put the inalienable right of all humankind to be free and to be equal.
"I worked with him closely, and remember well his visits to Downing Street. He was a wonderful man to be around, with a sharp wit, extraordinary political savvy and a lovely way of charming everyone in a building.
"He would delight in making sure that the person on the door or serving the tea would feel at home with him and be greeted by him with the same kindness and respect he would show a leader. So the warmth of his personality was equal to the magnitude of his contribution to the world.
"He was a great man, a great leader and the world's most powerful symbol of reconciliation, hope and progress."