Foreign Office officials have repeatedly told the inquiry, sitting in central London, British intelligence had no evidence of any connection between them.

But giving evidence on day three of the inquiry, the former British ambassador to Washington, Sir Christopher Meyer, said Mr Blair had directly linked the two following a private meeting with President George Bush at his Texas ranch.

He also contrasted Mr Blair's handling of the Iraq conflict unfavourably with the way he believed Margaret Thatcher would have dealt with it.

"I think she would have insisted on a coherent diplomatic strategy and I think she would have demanded the greatest clarity about what the heck would happen if and when we remove Saddam Hussein," he said.

Sir Christopher said that initially, when the Bush administration came to power in January 2001, there had been little talk in Washington of regime change in Iraq, even though it had been official US policy dating back to 1998.

"It was like a grumbling appendix," he said.

However, after the 9/11 attacks on the Twin Towers "everything changed".

By the time Mr Blair met Mr Bush seven months later, in April 2002, at the President's ranch in Crawford, Sir Christopher said there would have been no point in "banging on" about "regime change" only to say Britain would not support it.

He said that it was still unclear exactly what the two leaders discussed in private, but afterwards there was an apparent shift in the British position.

"I took no part in any of the discussions and there was a large chunk of that time when no adviser was there," he said.

"To this day I am not entirely clear what degree of convergence was, if you like, signed in blood at the Crawford ranch."

The following day, however, Mr Blair made a speech in which he spoke publicly for the first time about regime change in Baghdad.

"What he was trying to do was to draw the lessons of 9/11 and apply them to the situation in Iraq which led – I think not inadvertently but deliberately – to a conflation of the threat posed by Osama bin Laden and Saddam Hussein," he said.

"When I heard that speech, I thought that this represents a tightening of the UK/US alliance and a degree of convergence on the danger Saddam Hussein presented."

Sir Christopher said Mr Blair had always been a "true believer about the wickedness of Saddam Hussein" having made a speech on the subject as far back as 1998. But the Foreign Office had ruled there was no legal basis for seeking to oust the Iraqi dictator and, prior to the Crawford meeting, Mr Blair had generally been "discreet" about his views.

Sir Christopher said the British priority was to get a new United Nations Security Council resolution to provide the basis for military action and overcome the objections of the Foreign Office lawyers.

Although they had won support of a new Security Council resolution in November 2002, the strategy was ultimately a failure because weapons inspectors had not been given enough time to complete their work.

Sir Christopher said the "real problem" was that the US military was planning for an invasion in March 2003 which left the British and Americans "scrambling" to find proof Saddam had banned weapons of mass destruction in time.