The former prime minister, who worked with Mr Bush in the coalition to expel Iraqi dictator Saddam Hussein from Kuwait in the 1991 Gulf War, said it was a “privilege” to have known him.
“Sometimes people think politics is tawdry. You could have never have said that about the way George Bush behaved in politics. He had opponents but never enemies,” he told the BBC Radio 4 Today programme.
“He certainly was a man who made sure politics was a respectable profession and he understood its obligations to everyone, not just the powerful, not just the rich, not just the mighty, but to the people who were absolutely at the bottom of the heap as well.”
Theresa May said Mr Bush’s ethos of public service had been “the guiding thread of his life and an example to us all”.
“At each stage of his remarkable career, the president worked side by side with his friends, colleagues and counterparts in the United Kingdom,” she said.
“Today Britain remembers a great statesman and a true friend of our country.”
Former prime minister Tony Blair said: “President Bush was an extraordinary and exemplary public servant, a man dedicated to his country, the values it stands for at its best and to making the world better, more stable and more peaceful.”
Former US President Barack Obama paid his condolences in a statement. He said: “America has lost a patriot and humble servant in George Herbert Walker Bush. While our hearts are heavy today, they are also filled with gratitude. Our thoughts are with the entire Bush family tonight – and all who were inspired by George and Barbara’s example.”
Sir John paid tribute to the way Mr Bush had recognised the need to assemble an international coalition to eject Saddam following the Iraqi invasion of Kuwait.
“The war would never have been so successful without the Arab members of the coalition. I cannot think of any president more likely to have drawn together such a coalition,” he said.
“To make sure it was cemented he also went to the United Nations to get a United Nations resolution.
“That meant that it wasn’t a Western imperialist, as people might have said, attacking Iraq after their invasion of Kuwait. It was an attack by people representing every part of the world, and, in particular, Middle Eastern members of the coalition
“That was a remarkable piece of diplomacy I think very few presidents would have been able to achieve.”
Sir John said their alliance had led to a lifelong friendship which continued for years after they had both left office.
“The first phone call I had as prime minister was from George Bush,” he said.
“The first phone call I had seven years later when I was defeated was from George who said ‘Come over to Maine, the blue fish are biting, come and spend a few days with us’. So it did become a personal friendship.”