Prime Minister Tony Blair has paid tribute to John Paul II, saying he was "an inspiration, a man of extraordinary faith, dignity and courage".
Blair spoke of his family's meeting with the Pope
He said through an often difficult life, he had stood for social justice and on the side of the oppressed.
Conservative leader Michael Howard said the sense of loss felt by Catholics "will be shared by millions more".
Liberal Democrat leader said John Paul II was "a pivotal presence on the international stage".
All the main political parties have said they are suspending public election campaigning on Sunday in the wake of the Pope's death.
In a statement issued by Downing Street on Saturday, Mr Blair described the Pope as a "remarkable man".
The Pope is remembered for his fight against communism
"Yet whatever his own hardship and experience of what was wrong in human nature, he never lost faith in the human spirit and its ultimate capacity to do good," the statement said.
"To anyone fortunate enough to meet him, as I was with my family two years ago, he radiated such warmth and kindness that the meeting was unforgettable.
"He will be remembered with profound respect and admiration," Mr Blair said.
Conservative leader Michael Howard said: "In a world of change and uncertainty, people saw him as a rock: steadfast in support of freedom, unswerving in opposition to totalitarianism, robust in defence of Christian values.
"The Catholic Church has lost a truly remarkable Pope, and the world a very great spiritual leader."
Liberal Democrat leader Charles Kennedy said: "The papacy of Pope John Paul II will be remembered rightly as a historic turning point in European and world affairs.
"His was a pivotal presence on the international stage and he took his Christian message of hope to millions across the world."
Former Prime Minister Baroness Thatcher described him as the greatest pontiff of modern times and the "moral force" behind victory in the Cold War.
She said: "By combating the falsehoods of communism and proclaiming the true dignity of the individual, his was the moral force behind victory in the Cold War."
Constitutional expert Lord St John of Fawsley, one of Britain's leading Roman Catholics, described Pope John Paul II as the "greatest spiritual leader of the 20th Century".
"His condemnation of war whether in Northern Ireland or Iraq was absolute.
"So was his upholding of the rights of the unborn child and protection of the terminally ill and dying."
Scottish First Minister Jack McConnell said Scots have fond memories of his visit to Scotland in 1982.
"His passing will leave a big gap on the world stage," he said.
Conservative MP Ann Widdecombe, a convert to Roman Catholicism, said: "It will come as a relief that his suffering is over, but the effects of his reign are going to be felt for a very long time to come."
Democrat Unionist Party leader, the Reverend Ian Paisley, who had opposed the Pope's 1982 Scotland visit, said he understood how Catholics must feel following the pontiff's passing.
"We need to learn that everyone on earth no matter what position he holds or the claims he makes or the support he has must come to death and eternity.
"We can understand how Roman Catholics feel at the death of the Pope and we would want in no way to interfere with their expression of sorrow and grief at this time."
John Reid, Secretary of State for Health, who met the Pope in December 2000 when he was Secretary of State for Scotland, said John Paul II had "taken the papacy out to the world".
"In the midst of our Western affluence, he reminded us constantly of the plight of the poor, the underprivileged and the starving of the world and, above all, of our moral obligation to care for them."
Deputy leader of the Conservatives and the party's senior Roman Catholic, Michael Ancram, described John Paul II as "the People's Pope".
"He was an exemplary teacher to his church, a truly good shepherd to his flock."