Amid numerous reports of families being turned back from ports in northern France, firms have told The Independent they are bound by a two-decade old law.
Under the Immigration and Asylum Act 1999, carriers can be fined £2,000 “for each inadequately documented arrival”.
People covered by the laws include those without a visa, or with one that is expired or not yet valid.
A spokesperson for Eurotunnel said it was “helping increasing numbers of Ukrainian refugees to cross the Channel”.
“The UK government requires carriers to verify if passengers have the documents necessary to enter the UK before allowing them to board,” a statement added.
“To avoid the carrier liability fine, a support centre has been set up in Calais, to help Ukrainian refugees to obtain the correct papers before they cross.
“If someone arrives at our terminal without the papers they need to satisfy UK immigration requirements, with the town of Calais, we facilitate their transport to the support centre and then carry them once their papers are in order.”
Eurostar, the separate passenger train service that operates from European cities including Paris to London, said it required Ukrainian refugees to have visas in place before tickets are issued.
“There would be no point in passing through the ticket gate without a visa only to be turned away moments later at the border,” a spokesperson told The Independent.
Ferry companies, including P&O and Brittany, are subject to the same requirements under the law, as are aircraft operators.
It comes after the French interior minister said that by Saturday, around 400 Ukrainians wanting to reach the UK had arrived in Calais, and at least 150 had been turned back and told to obtain visas at British embassies in Paris or Brussels.
Gerald Darmanin warned that delays and confusion could “push people to take small boats to cross the Channel to England” and urged Britain to set up a processing centre in Calais.
On Monday afternoon, Priti Patel told parliament UK had set up a “bespoke visa application centre en route to Calais but away from the port”.
The centre did not appear on the Home Office’s website and it was unclear whether it had started operation.
“We have staff in Calais, we have support on the ground, it is wrong to say we are just turning people back, we are not,” Ms Patel added.
“It is important we do not create choke points in Calais but encourage a smooth flow of people.”
The British government has so far announced two bespoke routes for Ukrainian refugees - a family scheme for some relatives of those already settled in the UK, and a separate sponsorship scheme.
Ms Patel told MPs more than 14,000 people have applied to come to the UK via the Ukraine family scheme visa.
The Home Office has not yet released any update on how many of those applications had been processed, amid reports of slow turnaround times, and the sponsorship scheme has not yet been opened.
Labour leader Sir Keir Starmer said: “The Home Office is in a complete mess about this - they keep changing the rules, the stories of what is actually happening on the ground contradict what the Home Office say.
“They have got to sort this out ... there should be a simple route to sanctuary for those that are fleeing for their lives.”
The UN Refugee Agency (UNHCR) said it was offering advice to the government to ensure Ukrainians already in the UK are able to stay legally, and that those with family can enter “in an expedited fashion”.
A spokesperson told The Independent other schemes, for Ukrainians without family ties to Britain, should be “as generous as possible as a complement to the EU’s Temporary Protection Directive”.
The UNHCR is calling for the UK to extend its current measures to allow more Ukrainians already in Britain to extend their visas, and enable all those living lawfully in the UK to sponsor their Ukrainian relatives - rather than those in “limited immigration categories”.
The agency said the sponsored humanitarian route announced must be launched as soon as possible, and then be “rapidly scaled up after launch to meet the rapidly growing needs in Eastern Europe”.
More than 1.7 million Ukrainians fleeing Russia's invasion have so far crossed into central Europe, according to UN figures, with more than 1 million received by Poland alone since 24 February.
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