The UK Government is currently focusing on helping British nationals leave Ukraine and aiding Ukrainians with immediate family members who are UK citizens.

“They can come [to Britain] under family migration routes,” a Whitehall source told The Telegraph, adding that applicants would be subject to checks. “We are keen to use the systems that are already in place.”

General Lord Dannatt, a former head of the British Army, said that “in principle we could/should help” people fleeing Ukraine but hoped any displacement would be temporary.

“Therefore those affected would be better placed to be offered safe sanctuary in neighbouring countries friendly to Ukraine,” he added.

Damian Green, a Tory MP, agreed that Britain should offer financial assistance to Poland to help it cope with an influx of Ukrainians in the “appalling circumstances” of an invasion.

Bob Seely, another Conservative, said that Russia had been known to “weaponise refugees to cause chaos” in Syria, warning: “They may deliberately drive refugees to make it difficult for the Ukrainians to get around.”

The Polish prime minister has said his country is preparing to cope with a major influx of refugees if Russia invades.

“If there is aggression, we are preparing to accept refugees,” Mateusz Morawiecki, Poland’s prime minister, said in an interview published on Monday. “We are making logistical preparations so that any migratory movements can be absorbed by Poland as much as possible.”

Although estimates of how many people could flee to Poland vary, the Polish government has said it is preparing for the worst.

Maciej Wasik, a deputy interior minister, said last month: “We must be ready to deal with the black scenario, so that is why the Interior Ministry has been taking steps so we are prepared for a wave of up to a million people that could appear on our eastern border.”

Mr Morawiecki also said Poland is prepared to send convoys of humanitarian aid to Ukraine if fighting breaks out.