Former British Prime Minister Margaret Thatcher and former U.S. president Ronald Reagan were an odd couple, as different in personality as chalk and cheese.

Yet for eight years of the Eighties - a period when the world order changed dramatically - their relationship dominated international politics.

Together they achieved great things, virtually forcing the Soviet Union to collapse and giving the West victory in the Cold War that had frozen world affairs ever since the end of World War II.

There was a view that both of these leaders were comfortable and cozy with each other, but a new book has exploded this myth.

According to the Daily Mail, the book authored by British historian Professor Richard Aldous, reveals that both Reagan and Thatcher squabbled like an old married couple - and worse than most.

Drawing on recently de-classified documents and the personal testimony of those who witnessed the Thatcher-Reagan relationship close-up, Aldous identifies all the many issues on which daggers were drawn and angry words exchanged.

Thatcher viewed Reagan as more of a hindrance than a help when it came to British interests.

“If I reported what Mrs Thatcher really thought about President Reagan, it would damage Anglo-American relations,” said one former ambassador in Washington.

There were many times when mild-mannered Ron nagged and harangued, never able to get a word in when Margaret was in full flow, pinned down mercilessly on the sort of policy details that were never his forte - felt the same about her.

That said, he took their disagreements better than she did.

When she was thundering at him down the phone line from London, he would hold the receiver up for his roomful of aides to hear. ‘Isn’t she wonderful?’ he would say.

The mutual admiration was real enough and evident from their first meeting in 1975, she the new and unexpected leader of the Tory Party, he a mere presidential hopeful from California.

“They fell into conversation as if they’d been friends for years,” said one witness of the encounter.

“They were peas in a pod,” he added.

Which wasn’t actually the case. The truth is that they were fundamentally very different in style and personality.

Reagan was anecdotal, always ready with a languid quip and a homespun story, while Thatcher was policy-driven and intensely analytical.

They were not a match made in heaven. But they meshed nonetheless, drawn together because they were both outsiders in the corridors of power in Washington and London.

Washington’s liberal elite looked down their noses at right-winger Reagan, while the essentially male British establishment was never at ease with the Iron Lady.

Their first falling-out was over U.S. sanctions on the supply of technical equipment to Iron Curtain countries, nominally in protest at the crushing of dissent in communist Poland but in reality as a result of his new determination to stand up to Moscow.

The gesture endangered British companies with a 200 million pound stake in building a trans-Siberian gas pipeline, and Thatcher was blistering in her protests to Washington.

The next falling-out was over Argentina’s 1982 invasion of the Falklands. Thatcher stood her ground and refused all requests to halt her naval task force as it ploughed southwards to retake the islands.

The Reagan administration refused to support Britain in the Falklands War. There was nothing to negotiate. The Falklands were British. Argentina had tried to steal them. She would restore them to British ownership.

But with Britain’s defeat of the Argentine forces, Thatcher was back in the driving seat. She had shown the world she would not be pushed around. Reagan could not disguise his admiration, even envy. On her next visit to Washington, she was as pushy and assertive as ever.

Perhaps that was why, when in 1983 he approved the U.S. invasion of the Caribbean island of Grenada, a former British colony which was in thrall to Cuba and the Soviets, he deliberately didn’t tell her until it was too late.

When she discovered the truth, she was furious – ‘dismayed and let down,’ as she put it, ‘after all I’ve done for that man’.

She could push and prod him as much as she liked, hog the conversation, bully him, even. Secretly, she thought him her intellectual inferior. Often, he disappointed her.

But he was the main man. He had the power, and, however tough and clever she was, the best she and Britain could hope for was an honoured place on his coat-tails. This became crystal clear in dealings with Moscow.

Reagan shaped his Cold War strategy around a belief that the Soviet Union was doomed to the ash heap of history.

He also had a vision of a world without nuclear weapons. Thatcher, on the other hand, believed in staying armed to the hilt, with the threat of mutually assured destruction the guarantee of peace.

Thatcher was suspicious of Reagan's conciliatory stance towards Moscow

Reagan’s tactics for dealing with her, he explained, was that ‘she’s a woman and she has a lot she wants to say, so I just let her do it.’

But in the end he brought her to a juddering halt. In another meeting, she went too far with her scolding and her undermining of his position.

He looked her in the eye and stared her down. Around the table, no one moved.

Later, a presidential aide took her aside to warn her that if she spoke in public the way she had just addressed Reagan in private, it would do huge damage. If she chose to disagree with his nuclear strategy, it would be disastrous for him and, in turn, for Anglo-American relations.