Things could be a lot worse for Tony Blair. The war with Iraq could have gone badly wrong, with thousands of casualties among British troops. It could still be dragging on, with no end in sight. It could have coincided with large-scale terrorist attacks on Britain. As it was, while the terrorist threat remains, the war went remarkably well. It was over more quickly than even the optimists expected. Humanitarian relief is going into Iraq and the country is gradually becoming governable.

Yet Mr Blair finds himself under intense pressure. He told us Iraq’s chemical, biological and possibly nuclear weapons were an immediate danger to the outside world and to Saddam Hussein’s own people. In parliament last September he cited an intelligence picture “accumulated over the last four years” that Saddam had “active military plans for the use of chemical and biological weapons, which could be activated within 45 minutes . . . and that he is actively trying to acquire nuclear weapons capability”.

The prime minister’s claim that Saddam could use his lethal weapons in 45 minutes was electrifying. Within much less time it had flashed worldwide and was being broadcast on television and radio stations across the globe. In America it was said that Mr Blair was making the case for action against Iraq more effectively than George W Bush. It looked like British intelligence’s finest hour.

But it wasn’t. The 45-minute claim was indeed included in the evidence submitted by Whitehall’s joint intelligence committee (JIC) to Downing Street but it was based on a single, possibly unreliable, source. For Alastair Campbell, however, the prime minister’s tabloid-trained director of communications and strategy, it was the golden nugget buried deep in the JIC’s carefully qualified statements. Once spotted it was given the prominence that, in No 10’s view, such a sensational piece of information deserved; it was, to put it bluntly, “sexed up”.

That 45-minute claim now looks increasingly absurd. It is far too soon to conclude that chemical and biological weapons, or the capacity to make them, will not be found in Iraq. The effort to find them is being stepped up and Mr Blair may yet be vindicated. But the idea they were so accessible that Saddam could use them at will looks far fetched. On this and other matters, the September dossier went too far. Downing Street appears to have realised quite quickly it could not rely on the intelligence services to make the case against Saddam. In February, Mr Campbell’s unit produced an explicitly “sexed up” document, the famous “dodgy dossier” that included extracts from a 12-year-old doctoral thesis. On March 18, in the eve-of-war Commons debate, Mr Blair drew his evidence from the report by Hans Blix, the chief United Nations weapons inspector.

That does not get him off the hook. Clare Short, the former international development secretary, says the prime minister “duped us all along”. In America, where leaks of Defense Intelligence Agency reports suggest evidence of Saddam’s weapons was not conclusive, the issue is also live but Mr Bush is under less pressure. There was much more hostility to the war in Britain and it needed the prime minister’s claims about the dangers posed by Saddam’s weapons to persuade wavering voices. But the consequence is a serious blow — trust, Mr Blair’s most precious political commodity, is ebbing away fast.

The prime minister has conceded an investigation by the intelligence and security committee but it is unlikely to bite the Downing Street hand that appoints it. The foreign affairs select committee is to launch an investigation but it too falls short of the full independent committee of inquiry needed. Margaret Thatcher had such an inquiry under Lord Franks after the Falklands war two decades ago. Mr Blair should do the same, otherwise the electorate will form the understandable opinion that he has something to hide. Last September he insisted in the House of Commons that the existence of Saddam’s weapons of mass destruction was “not American or British propaganda”. The onus is on him to prove it.