Fifty Ukrainians have been granted visas under a scheme for refugees with family links to the UK, the Home Office has announced.
It is about 1% of the 5,535 people who have applied since the programme launched 48 hours earlier.
Europe minister James Cleverly said he did not know the exact figures but said numbers would increase “very quickly”.
The Ukrainian ambassador praised the UK effort but urged for the “maximum” number of people to be admitted.
Home Secretary Priti Patel said she was “doing everything possible” to speed up efforts to issue the travel permits.
The UK has steadily increased its visa offer to refugees from the Ukraine war, extending it to parents, grandparents and siblings as well as “immediate family” and extending the visas to three years.
But it has faced criticism that its scheme is less generous than the European Union’s, while France accused the UK of a “lack of humanity”, saying that 150 refugees were turned back at Calais for lacking a visa.
Earlier this week, Prime Minister Boris Johnson said 200,000 Ukrainians would be eligible to travel to the UK as he extended the offer of visas to a wider range of family members.
As of 10:00 GMT on Sunday, the Home Office said 11,750 had begun applications online, while 5,535 had completed them.
It added that 2,368 had booked a visa appointment to submit their application and biometric information, while “around 50” visas had been granted.
Mr Cleverly told BBC Breakfast the final figure would be “significantly” more than the 50 figure being quoted and said while a process was needed the government would make it “as quick, easy and as fast as possible”.
“We are looking to create something very, very large-scale very, very quickly” he said. “Initially it will be slower than we would like but that will pick up.”
Asked if it was acceptable that about 1% of applications had been granted in the first 48 hours of the scheme, Ms Patel said it was “the first scheme in the world that’s up and running in this short period of time”.
“This is an incredible scheme and we are doing everything possible, surging capacity across every single application centre across the EU,” she said, adding that staff were being flown into Ukraine’s border countries to speed up applications.
Ukraine’s immediate neighbours have taken in the majority of the 1.5 million people estimated to have fled the war, with more than one million arriving in Poland.
Mr Celverly said that while “all of us would want to throw our arms open and be generous” there needed to be a process but there was no upper limit on how many Ukrainians could come to the UK via government schemes.
“We want to play our part but of course most Ukrainian refugees are in the countries bordering Ukraine and that’s where they want to stay and we are providing humanitarian support for them there as well,” he said.
‘Not turning people back’
France’s Interior Minister Gerald Darmanin wrote to Ms Patel on Saturday, saying that 400 Ukrainian refugees had arrived at Calais to cross the Channel, but 150 were sent back and told to obtain UK visas at embassies in Paris or Brussels.
Mr Darmanin said the response to people in distress was “completely unsuitable” and showed a “lack of humanity”, calling for the UK to put consular staff at Calais to help Ukrainian refugees cross.
But Ms Patel said it was “wrong to say we are turning people back” and said the Home Office already had people working in Calais to support Ukrainian families.
The Sun reported that Ms Patel was “investigating legal options” to create a humanitarian route, which would mean anyone without ties to the UK fleeing the conflict would have the right to come to the UK.
However, the BBC understands this referred to the already announced route where refugees can be sponsored by individuals, communities or organisation and Mr Cleverly confirmed that there had been no change to the government’s policy over the weekend.
Vadym Prystaiko, Ukraine’s ambassador to the UK, said that the visa process could be simplified, adding that any issues could be resolved later but right now the “maximum” number needed to be admitted.
He said any “bureaucratic nonsense” should be cleared away, although he said it was necessary to continue security checks.
But he said the UK was at the “forefront of the effort” to support Ukraine.
On Monday the Disasters Emergency Committee announced its Ukraine appeal had raised more than £100m in four days.