Not joining the coalition would have had serious consequences. It took a lot of forcing to get the Americans to the UN and a resolution passed.
United Nations Security Council Resolution 1441 is a United Nations Security Council resolution adopted unanimously by the United Nations Security Council on 8 November 2002, offering Iraq under Saddam Hussein "a final opportunity to comply with its disarmament obligations" that had been set out in several previous resolutions (Resolution 660, Resolution 661, Resolution 678, Resolution 686, Resolution 687, Resolution 688, Resolution 707, Resolution 715, Resolution 986, and Resolution 1284).
Resolution 1441 stated that Iraq was in material breach of the ceasefire terms presented under the terms of Resolution 687. Iraq's breaches related not only to weapons of mass destruction (WMD), but also the known construction of prohibited types of missiles, the purchase and import of prohibited armaments, and the continuing refusal of Iraq to compensate Kuwait for the widespread looting conducted by Iraqi troops during the 1990–1991 invasion and occupation. It also stated that "...false statements or omissions in the declarations submitted by Iraq pursuant to this resolution and failure by Iraq at any time to comply with, and cooperate fully in the implementation of, this resolution shall constitute a further material breach of Iraq's obligations."
Notice "unanimously". The Blix report to the UN SC of Jan. 27 2003 is a catalogue of Iraqi non-compliance with the inspectors and thus Resolution 687 (1991), which was still in force, legally justified military action. Resolution 1441 (Nov 2002) specifically stated that Iraqi was in material breach of 687. And Blix agreed.
The US had 250,000 troops in the region which couldn't be held in readiness while a diplomatic dance took place possibly lasting until the ghastly summer arrived and, in effect, giving Saddam victory which he would have played for all it was worth in the Arab world.
For sure the unintended consequences of military action were bad. But they have to be set against any unintended consequences of Saddam remaining in power indefinitely. That's the moral argument. Not to compare the consequences of action against nothing.
It was a tough call but we elect these people to make tough calls and when they do we should accept them as having been made in good faith. How tough they are is pointed up by Mr Obama's 2008 election promise to close Gitmo and here he is starting his 2nd term with it still in full swing.
After the pussy-footing with Hitler and Nasser people had become impatient with the likes of Saddam.
As far as I'm aware the UK had nothing to do with rendition.