For days pundits of international etiquette have been offering advice on the right response when the president of the United States greets you with: “Yo, Blair! How are you doing?” Whether the prime minister should have exchanged high fives or a “Hi, George, how’s it hanging?”, he blew it. Faced with George Bush’s frat boy bonhomie, Tony Blair retreated into an English middle-class incoherence. It might have been endearing from Hugh Grant; it was unbecoming for a prime minister.

It may be, as Downing Street says, that the informality told of the strength of their relationship. Perhaps, but it also told of a special relationship that has degenerated into one of master and servant. Mr Blair has always seemed in awe of Mr Bush and his power, far more than he was of Bill Clinton. His incoherence was bad but his subservience was worse. What do we make of it when the prime minister offers to go to the Middle East to try to mediate in the Israel-Lebanon crisis, risking humiliation, just to pave the way for Condoleezza Rice, the secretary of state? Or worse, when the president effectively tells him not to bother? Mr Blair’s tone, as one US columnist wrote, was “more like an over-eager White House intern than the leader of a sovereign nation”.

The prime minister’s relationship with Mr Bush was forged in the days after the 9/11 attacks on America. After declaring, rightly, that Britain would stand shoulder to shoulder with Washington, Mr Blair contrived to put himself into the position of never being able to say no. A second United Nations resolution on Iraq, the prime minister’s bottom line ahead of the invasion three years ago, was never seriously pursued by the White House. Instead Mr Blair was fobbed off with the promise of a new drive for peace in the Middle East. Recent events show how shallow that was.

It may never have been possible to prevent the bloody insurgency in Iraq, but America’s lack of post-war planning and the prime minister’s reluctance to force the issue were a significant factor. The worrying situation in Afghanistan reflects both a failure to finish the job and conflicting US and British tactics on the ground. Does Mr Blair hammer the table and tell his ally what for? There is no sign of it.

Sir Christopher Meyer, the former ambassador to Washington, wrote in his memoirs about his frustration at Mr Blair’s failure to engage the president in “plain-speaking conversation”. He wrote: “The high moral ground, and the pure white flame of unconditional support to an ally in service of an idea, have their disadvantages. They place your destiny in the hands of an ally . . . They discourage descent into the dull detail of tough and necessary bargaining: meat and drink to Margaret Thatcher but, so it seemed, uncongenial to Tony Blair.”

The contrast between Mr Blair now and Mrs Thatcher then is striking. She battled with the White House over the Falklands and Grenada. She prevented Ronald Reagan making overgenerous concessions to Mikhail Gorbachev at Reykjavik, and stiffened a wobbly George Bush Sr’s resolve ahead of the first Gulf war. She also took flak at home for supporting him over the deployment of cruise missiles and the bombing raid on Libya. She earned America’s respect. After an ear-blasting tirade Mr Reagan would turn to his officials and say how marvellous she was.

Most of Mr Blair’s instincts in supporting America have been right. He is right not to demand a ceasefire in Lebanon while Hezbollah plans more mayhem and Iran seeks to take leadership of the Islamic world. But the special relationship between Britain and the United States flourishes only when Britain’s leader is more bulldog than poodle. That would enhance our international position and convince Mr Blair’s supporters that he really is punching above his weight and not becoming a flyweight in a heavyweight world.