The organisations are urging the prime minister to put pressure on the US to enter talks with Tehran.
The US has refused to rule out military action if Iran does not halt its nuclear activities.
Former Labour MP Lorna Fitzsimons warned that time was “running out” to stop Iran becoming nuclear-armed.
Criticism
The US and its Western allies suspect Iran of using its nuclear energy programme as a cover to produce atomic weapons. Tehran denies this claim.
Recent criticism by President George Bush of alleged Iranian support for insurgency in Iraq has increased concerns that his administration is contemplating an attack.
In the report, Time to Talk: The Case for Diplomatic Solutions on Iran, the coalition accuses Mr Blair of using the prospect of military action as a negotiating tool.
Launching the report, former Labour minister Stephen Twigg, director of the Foreign Policy Centre, said: “The consequences of military action against Iran are not only unpalatable; they are unthinkable.
“Even according to the worst estimates, Iran is still years away from having a nuclear weapon.
“There is still time to talk and the prime minister must make sure our allies use it.”
Coalition
The charity Oxfam, unions Unison, GMB and Amicus, have been joined by the Muslim Parliament and Christian Solidarity Worldwide in signing the report.
They warn that a strike against Iran would continue to destabilise the region and provoke further attacks against British forces in Iraq and Afghanistan.
“Military action is not likely to be a short, sharp engagement but could have a profound effect on the region, with shock waves felt far beyond,” the report says.
It goes on to say the British government is “well positioned to articulate objections to military action” and that it should “not lose this opportunity to advocate for direct US engagement”.
But Ms Fitzsimons, chief executive of the Britain-Israel Communications and Research Centre, told BBC Radio 4’s Today programme: “What we are talking about here is Iran reaching the ability on an industrial scale to manufacture highly enriched uranium.”
‘Watershed’
International Institute for Strategic Studies and others were predicting this would happen within 11 months, she added.
Ms Fitzsimons said: “That is the watershed. There is no return from that point.
“You can’t get the genie back in the bottle technologically once they have sorted out the problem they currently have with their centrifuges.
“I don’t think you can stop it. You might be able to disrupt it. It’s a question of looking at how far you can go down the line where you lose the ability to disrupt it.”
Sir Richard Dalton, the British ambassador to Iran until last year, backed the calls for increased diplomacy.
“Recourse to military action – other than in legitimate self-defence – is not only unlikely to work but would be a disaster for Iran, the region and quite possibly the world,” he said.
Military warnings
Liberal Democrat foreign affairs spokesman Michael Moore said: “This is a timely and significant report.
“It highlights the need for the international community to be more aware of the potentially disastrous consequences of military action against Iran.”
But the Conservatives said it was important to “keep all options on the table”.
Shadow defence secretary Liam Fox said: “We cannot give them the comfort of believing that there is any weakness in the western alliance or that there is a chance that they might be able to divide and rule.”
