Western officials fear the number of refugees fleeing Ukraine could hit 4 million as Russia continues its brutal onslaught.
The UN refugee agency briefed Western countries on Wednesday that there were now an estimated 2.2 million refugees from the conflict - and the number could rise to 4 million over the days to come.
Officials say the Russian invasion has sparked almost "unprecedented" movements of people across Europe, triggering the greatest refugee crisis since the Second World War.
One said: "I would like to stress the sheer scale of this, which is something that we haven't seen, certainly since the end of the Second World War, and that is a real challenge to us all."
It comes as Home Secretary Priti Patel was forced to streamline the visa process for Ukrainian's seeking sanctuary in Britain after a public outcry.
Refugees are turning up with frostbite from the cold as they are often forced to make the treacherous journey on foot.
Others are traumatised or in need of medical care after facing the Russian bombardment.
The first wave of refugees moved quickly on from Ukraine as many of them had contacts and resources in other countries, officials said.
But the group of people now trying to flee are traumatised by the horrors they have witnessed and have often left everything behind.
Those turning up more recently were the "more infirm, for example the elderly, the grandparents who people have left behind because they are not able to move around very easily".
One official said: "What we're seeing is with the refugees now and the IDPs (internally displaced persons), you're getting simple things like frostbite because people are walking.
"You're getting things like women who can't get access to maternal healthcare, you're getting people needing mental health support because they've just come from areas that have been targeted and bombed. So, the needs are going to keep shifting."
Officials are struggling to verify figures on casualty numbers and those who have been internally displaced in Ukraine.
They are particularly concerned about Russian bombardment of hospitals, including 18 verified attacks on ambulances and other healthcare facilities across Ukraine.
Priti Patel promised refugees would be able to apply online for visas after criticism of the Home Office's chaotic approach.
She told MPs the changes will come in from Tuesday following assurances from the security services that the UK can still be protected from Russian efforts to infiltrate the country by posing as Ukrainian refugees.
