By Jon Leyne BBC News, Amman

Millions of Iraqis have been forced out of their homes by the conflict

But this country now plays host to up to one million Iraqis who have fled the fighting in their country. Up to a million are in nearby Syria.

And there are big numbers in Iraq's other neighbours.

After nearly four years of war, they know they are not about to return home any time soon. The hidden crisis is beginning to demand the world's attention.

At Jordan's desert border crossing with Iraq, you see the Iraqi families arriving. Their belongings are piled high in GMCs, big American 10-seater vehicles that race across the badlands of western Iraq.

You've got to ask how long this generosity can continue before they start closing the borders Andrew Harper

The Iraqis here will tell you of their relief after running the gauntlet of American soldiers, Iraqi insurgents, and the many bandits, that make this one of the most notorious journeys in the world. This wind-blown border post, many kilometres from the nearest town, is their safe haven, their refuge.

But Jordan is only letting in a fraction of the numbers it used to, perhaps only 10 or 15 car loads a day.

Divided families

One old man I met just inside the border, who was arriving for medical treatment, was furious after a young nephew travelling with him was turned back by the Jordanians.

Almost all Iraqis you speak to have tales of how much more difficult it is to get into Jordan, compared with just a few months ago.

Iraq's capital and much of the central region is hit by daily violence

"It's very difficult to get people outside of Iraq," explained Lutfi, an Iraqi doctor who has just managed to help his father join him in Jordan.

"I used to come easily, there was no trouble at all. But lots of things have changed. Most of the Iraqis are forbidden to come unless they have something to prove they are studying, or for business or investment."

The Jordanian government says there has been no formal change of policy; but a spokesman said there had been a tightening of regulations, particularly for security reasons.

Precious passports

It is a trend echoed around the region. Kasra Mofarah works in Jordan coordinating aid agencies operating in Iraq.

"Most of the borders of the neighbouring countries of Iraq are very difficult to pass. They have administrative problems, passport issues, and they are not welcome any more," he explained.

"Also the Western countries and the wealthier countries, they are becoming more and more difficult in terms of allocating any visa, or allowing any entrance. So it seems the doors are closing one by one around the world on the face of Iraqis."

It's even harder to move on from Jordan. Britain and the United States have just introduced new rules, invalidating most Iraqi passports.

Even Iraqis who have managed to get one of the prized new G-series passports will be even luckier if they can get a visa.

Ashraf worked for an American company in Baghdad. He decided to get out after being kidnapped twice. Now he is stuck in Jordan:

"I applied for a visa to go to the UK and also to the States. I got rejected many times by the British government and the American government.

"They are pretty much responsible to help people like me and other friends that I know that worked with the military or the Americans."

'Sent to die'

Lina and Nasir are two Iraqi doctors, who travelled to Britain to study in order to further their work on the mass graves where victims of Saddam's regime are buried.

The insurgents tracked them down and started sending terrifying threatening emails.

They were refused even an extension of their visas to stay in Britain, and were told not to bother even applying for political asylum.

"It's unbelievable", said Nasir. "If you just send me home you send me to die. It's a matter of life or death, it's nothing in between."

Returning to Iraq could be a death sentence, some refugees fear

In fact the number of Iraqis being granted refugee status or political asylum in Britain has actually gone down since the invasion in 2003.

Only five Iraqis were granted refugee status by the British government in 2005.

It's the most graphic illustration of the world's neglect of this growing crisis.

Slipping into poverty

Jordan itself has been widely praised for its tolerance in allowing in so many Iraqis. But Andrew Harper of the UN refugee agency warned that its a situation that cannot go on for ever.

"You've got to ask how long this generosity can continue before saturation and before they start closing the borders," he warned. "And once they are closed, what then happens to those refugees who are trying to escape from Iraq?"

In Jordan itself, most Iraqis are not allowed to work. Apart from a few rich businessman, they are slowly sinking into poverty.

Schooling is difficult, medical care even more precarious.

Dr Lutfi is trying to support the family he has managed to get out of Iraq. But he can't earn money here.

After being turned down for visas by Britain, the USA and Sweden, he decided there was no option but to return to Iraq and find work there.

A desperate remedy for an increasingly desperate situation.