It was a far cry from what they had left behind - after a week stranded in squalid limbo outside Budapest's main railway station thousands of refugees crossed from Hungary into Austria on Saturday and received something they had been missing: a warm welcome.

Along with much-needed dry blankets and cups of hot tea, Austrian aid workers dispensed smiles to the refugees as they trudged through the border crossing in the town of Nickelsdorf in the pouring rain, many carrying their children and their entire worldly possessions in their arms.

For those too exhausted to go on, there were clean cots to sleep on at a hastily set up reception centre in the town's Nova Rock concert hall; for those who wanted to keep moving, there were trains to Salzburg, Munich and beyond.

For the first arrivals shortly after 5am, it was the victorious end of a long march that had begun on Friday morning in Budapest when more than 1,000 of the migrants from outside the Keleti railway station in Budapest took matters into their own hands and decided to walk to Vienna.

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The tactic worked, disrupting the traffic on Hungary's main M1 motorway to the Austrian capital and forcing the Hungarian government to capitulate in a night of political drama that - temporarily at least - relieved one of the ugliest pinch-points of Europe's migrant crisis.

After a late evening phone-call between Austria's chancellor, Werner Faymann, and Viktor Orban, Hungary's hardline, anti-immigrant prime minister, buses were sent to pick up the marchers, while others still in Budapest were offered transport to the border.

As they arrived, many vented their anger at their treatment by Hungary, with one saying the country should be "fired" from the EU. Another said they "felt like they could breathe again" after a week being stuck in Budapest.

For them, and men like Ahmad Ahmadi, a 28-year-old from Jalalabad, Afghanistan, the Austro-Hungarian border represented not just the physical barrier between two countries, but the moral divide over how to deal with the migrants now pouring in from Afghanistan and the Middle East.

"I don't know why Hungary has treated us so badly," he complained to The Sunday Telegraph, "they have been very cruel. But here in Austria the welcome has been very nice. They are helping us, because they know we have no other place to go."

Mr Ahmadi, who says his final goal is to reach Italy, was among a group of 2,000 refugees who this week refused to get off a train in the town of Bicske until they were guaranteed passage to Austria, spending 28 hours on the train with only water and no food.

Migrants arrive at the Hungarian-Austrian border in Nickelsdorf, Austria. Photo / AP
Migrants arrive at the Hungarian-Austrian border in Nickelsdorf, Austria. Photo / AP

He rejected the Hungarian government's contention that the majority of those at Biscke and Keleti are really economic migrants who could still live safely in cities like Kabul, or the refugee camps in Turkey, but choose Europe principally for the economic opportunities.

Mr Ahmadi, a Pashtun man travelling with a cousin and nephew, said his late father was a local military commander who made enemies that put his life at risk. "We are not safe, the Taliban are very cruel," he added, "we have no choice. If I could live safely in Afghanistan I would stay."

It is men like Mr Ahmadi and their families who exist in the grey area between war refugees and economic migrants, that this week became pawns in a stalemated game of European political chess over how best to handle the migrant crisis.

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While Austria, Germany and the European Commission exhorted all European members to do more to help the refugees and embrace national quotas for up to 160,000 - the poorer Eastern European states like Hungary, Poland and the Czech and Slovak Republics rejected the proposal.

There was no sugar-coating the depth of the divide between the two camps, who both appealed to two very different concepts of what "European values" actually mean.

"Europe for me is and always has been a community of values," wrote Jean-Claude Juncker in an article calling for greater compassion and proposing countries accept larger quotas, "We have the highest asylum standards in the world, which are inscribed in our laws and our treaties."

Migrants board a train to Budapest at the main railway station in Debrecen. Photo / AP
Migrants board a train to Budapest at the main railway station in Debrecen. Photo / AP

Those standards were not in evidence in Budapest this week, however, where the authorities did the bare minimum to provide for the migrants stuck in holding camps and in Keleti square after the international rail lines were shut down.

By midweek the smell of unwashed bodies wafting up from the subways under the main square was forcing elegantly dressed Hungarian women to clamp handkerchiefs over their mouths as they hurried past on their way to work or for a night out with friends.

With only seven portable lavatories for over 2,000 people and no washing facilities, the migrants quickly began to fit the fearful image created for them by Hungary's government which openly rejects the notion that "European values" means embracing multiculturalism.

Volunteers prepare food packets as they wait for trains with refugees at the Hauptbahnhof station in Salzburg Austria. Photo / AP
Volunteers prepare food packets as they wait for trains with refugees at the Hauptbahnhof station in Salzburg Austria. Photo / AP
Camp beds are prepared for arriving refugees at the Hauptbahnhof station in Salzburg, Austria. Photo / AP
Camp beds are prepared for arriving refugees at the Hauptbahnhof station in Salzburg, Austria. Photo / AP

A compassionate minority volunteered to help, handing out bedding rolls and playing games with the children, while activists on the left posted on Facebook about how uncomfortable it was given Hungary's wartime history, to see unwanted peoples being demonised and herded onto trains.

"This whole thing caused flashbacks to me," wrote András Jámbor, a left-wing blogger, on his Facebook page, "After all, I am still a Hungarian Jew, and yes, my extended family is short of a lot of members."

But in Brussels this week Mr Orban was unrepentant, visibly discomforting Europe's top officials as he spoke about a "Christian obligation" to signal to migrants they would not be welcome in Europe, warning later that soon "tens of millions" could make Hungarians a minority in their own country.

Donald Tusk, president of the European Council, warned at the start of the week that it would be "unforgivable" if a new east-west split developed in Europe over migration between "advocates of containment" and "advocates of full openness" but by Friday the cracks were getting increasingly impossible to conceal

As for the influx of Muslims into Europe from the Middle East's war zones, Mr Orban said bluntly that Hungary's 150-year experience as a province of the Ottoman Empire means that the country cannot cope with such stresses.

"We do not like the consequences of having large numbers of Muslim communities that we see in other countries, and I see no reason for anyone to force us to create ways of living together," he said at a press conference, "Therefore, there are differences."

Refugees arrive at the train station in Saalfeld, central Germany. Photo / AP
Refugees arrive at the train station in Saalfeld, central Germany. Photo / AP

That was a rare piece of understatement from Mr Orban, who ignored criticism in Brussels and pressed on with his agenda, passing laws strengthening the GBP80m razor-wire blockade on Hungary's border with Serbia.

"What else would you suggest we do?" retorted Zoltan Kovacs, the Hungarian government's chief spokesman when asked about the fence by The Sunday Telegraph, going on to ridicule Mr Juncker's quota system as unworkable, pointing out that Hungary had received 160,000 migrants this year alone.

It is a position that Mr Orban shows no signs of backing away from, announcing on Saturday that he was preparing to deploy the Hungarian army to bring the border under control "step by step".

Mr Orban's demands to fortify Europe's external border and his open rejection of Muslims on religious and cultural grounds is popular at home, with a survey this week from the Republikon Institute in Budapest finding that two-thirds of Hungarians believe refugees "pose a danger to Hungary".

Such sentiments are reflected in the success of extreme-right parties like Hungary's Jobbik who in April won their first seat in the Hungarian parliament and are becoming an ascendant voice in Hungarian politics, driving Mr Orban further to the right.

Márton Gyöngyösi, the deputy-leader of Jobbik's parliamentary grouping, was unapologetic about his party's calls to "defend Christian Europe" from African and Muslim migrants who he described as "a threat" to Europe's Christian civilisation.

The party held a rally at the border town of Roszke this week at which speakers warned that ethnic Hungarians would become "aboriginals in a museum showcase" unless the migrants were stopped.

Blaming the major European powers for triggering the migrant crisis with its mishandling of the Middle East, Mr Gyöngyösi said he was incredulous that countries like German and Austria could not appreciate the scale of the threat posed by uncontrolled migration.

"It is like Europe's immune system is failing," he told The Sunday Telegraph, "these countries do not sense the danger of what is happening. You British have experience with these Africans and Asians, you once ruled half the world, but our country has no such history."

The language of such coded racial discrimination - likening migrants to an infectious disease - might be deeply unpalatable, but it is fuelled by the visible failure of the European Union to develop a workable EU asylum policy and coordinate response to the crisis.

Long term solutions, such as beefing up security in the Mediterranean, reducing conflict in the Middle East and investing more in handling refugees before they reach the EU offer no immediate comfort to poorer EU countries like Hungary which was hit hard by the 2008 financial crisis.

With the average Hungarian's net monthly salary coming in at just 550 euros a month - less than a quarter of those in Germany or France - there is a demand for clarity, not confusion and open irritation at German largesse that, Hungary warns, it cannot afford.

"We have to secure the border - isn't that why you have a fence at Calais?" the government spokesman challenged, "this is just a double standard. It is Hungary that is following the Schengen Agreement by closing the border, not Germany by creating these misunderstandings."

The UN refugee agency (UNHCR) praised France and German for showing "political leadership based on humanitarian values", but in Hungary the decision to ignore the Schengen agreement and allow migrants to settle guaranteed only one thing - more migrants.

As Mr Juncker observed in an article this week, Europe fails "when fear prevails" and succeeds "when we work together, pragmatically and efficiently" to meet the challenges posed by the biggest migration crisis since the Second World War.

By that benchmark, this week in Budapest was a catalogue of failures, characterised by fears and confusion on all sides, forcing the migrants to march up a motorway in order to get action from authorities who - like it or not - owed them a duty of care.

That confusion was building again on Saturday night as more Syrian and Afghan migrants came to Keleti station hoping that more buses might take them to Austria, only for a Hungarian government spokesman to rule out any further transports.

And so it was by lunchtime that another 600 migrants set off on foot towards the M1 to Vienna, unsure if they would picked up by buses like those had been on Friday - and if not, then why not.

"Why are there are no buses?" asked Wasim Al Jubail, a 29 year old Syrian who left a holding camp for Keleti square after hearing of Saturday night's crossings into Austria. "We are very confused," he said, "We do not understand."

He is not alone.