Russia’s invasion of Ukraine has forced more than a million people to flee the war in just a week, an exodus so swift it almost matches the number of people who sought refuge in Europe in a whole year during the 2015 migration crisis.

Seven years ago, hundreds of thousands of Syrians fled their strife-torn country, which Russian also bombarded. Together with people escaping fighting in Afghanistan, Iraq and elsewhere, they headed west, with thousands dying at sea trying to reach a continent where many didn’t want them.

The arrival of about 1.3 million people sparked tensions among European partners as they squabbled over how many refugees and asylum-seekers to accept, and bolstered far-right populists, some of whom were friendly to the Kremlin.

But as Russian forces inflict massive destruction on a neighbouring nation today, Europeans have united in extending a helping hand.

In one week, they accepted more than 2% of Ukraine’s 44 million population, according to the United Nations refugee agency, UNHCR. The operation has gone relatively smoothly thanks to an enormous mobilisation of volunteers near and far who have gone to the borders to help — some from as far away as the United States.

One was Laura Bukavina, a Ukrainian-born doctor volunteering with the Cleveland Maidan Association, a group that arose to help Ukraine when it was first invaded by Russia in 2014. The group sent medical supplies to Ukraine and Ms Bukavina went to the border to provide medical assistance to Ukrainians evacuated to Polish hospitals.

The European Union decided on Thursday to grant people fleeing Ukraine temporary protection and residency permits. EU migration commissioner Ylva Johansson said millions more – UNHCR has predicted the war will produce up to four million refugees – were expected to move into the 27-nation bloc and would require shelter, education for the young and work.

Ms Johansson called the quick adoption of the protection rules a “historic result” and said “the EU stands united to save lives”.

The EU’s executive commission has promised at least 500 million euros (£414 million) in humanitarian aid for the refugees. Ms Johansson pointed to Poland’s welcome as an example for other nations to follow.

Meanwhile, Ukrainians and foreigners who had been living in Ukraine continued to disembark in Polish, Hungarian, Slovakian, Romanian and Moldovan border towns.

Among them was Nadia Zuravka, a teenager who arrived on Thursday in Przemysl, Poland, with her mother. They came from Ukraine’s second-largest city of Kharkiv, which is facing massive bombardment. She said both her school and her home had been hit by bombs and her friends were all hiding in basements.

“Everything of value to me” has faced some level of destruction, she said.

Poland, a neighbouring Slavic nation where many Ukrainians have settled in recent years for work, has received the largest single group of refugees so far — with many being taken in by relatives or Polish friends. The refugees also head for Ukraine’s other western neighbours, some moving on from there to countries like Italy and Germany, where many Ukrainians live.

In all cases, authorities and volunteers have met exhausted people at border crossings after bus and train journeys that take days. They serve food to the newcomers or guide them to shelters — and sometimes take strangers into their own homes.

They are taking in orphans and treating the sick in hospitals, including children with cancer who have been evacuated to hospitals in Poland.

Pope Francis publicly thanked Poland for its role in helping refugees from the war in Ukraine this week, praising the country’s people for “opening your borders, your hearts, the doors of your homes”.

People from across Europe are helping too, even as they struggle with their own fears of what this dangerous new chapter holds in store for a continent that has faced so much bloodshed in past wars.

Luc Dedecker drove 1,025 miles from his home in Belgium to Przemysl, stopping only to sleep in his car. He was prepared to take strangers back to his home.

“People need to be helped,” he said. He also described a profound fear of President Russian Vladimir Putin.

For Poles, Russia’s attack on Ukraine inevitably evokes memories of their own country’s double invasion in 1939 by Nazi Germany and the Soviet Union. The German invasion triggered the Second World War and a brutal five-year occupation that killed six million Poles, including three million Jews in the Holocaust.

Scenes of destroyed Ukrainian cities today recall the look of Polish cities levelled by German bombardments during the war.

Some described helping Ukrainians now as part of a struggle by the democratic West to defend their own liberty, since sheltering Ukrainian women and children frees the men to fight at home.

“We think that if Ukrainians fight and win, we will be safe. Now we are not safe,” said Bartosz Tomaszewski, a 28-year-old Pole in a yellow security vest that marked him as a volunteer.

He has been helping to guide people coming off trains in Przemsyl, travelling there each day from his home in the nearby city of Rzeszow.

Mr Tomaszewski fears that if Ukrainian President Volodymr Zelensky fails to stop Mr Putin, Poland would be the next target, along with the Baltic nations of Lithuania, Latvia and Estonia.

“Putin is a sick man, to me, he’s like Hitler,” Mr Tomaszewski said. “It would be World World Three.”