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The scheme opened on March 14, with the aim of allowing individuals, charities, community groups and businesses to bring Ukrainians to safety.
So far, 25,500 visas have been issued, which includes 22,800 permits under a separate family scheme, the Home Office said.
The UK has been accused of applying a slow and chaotic system for allowing refugees into the country. The Prime Minister defended the Government’s “overwhelmingly generous” when confronted with the charge paperwork is being put ahead of people.
“Everybody I think is pulling together, the number of people who have come forward to offer their homes is incredible," Boris Johnson said. “But I really don’t think that he should deprecate what the UK is offering. We have already given 25,000 people, have already got visas, we are processing 1,000 a day, and there is no limit, no upper limit to the number that we can take.
One charity supporting families fleeing Ukraine has accused the UK government of failing to issue any visas to hundreds of people it is helping to place in the homes of volunteers.
The charity, Positive Action in Housing, said it had been helping nearly 500 families and individuals, including unaccompanied children, to find a sponsor but none of them had secured visas.
More than four million people have fled the war in Ukraine, figures from the UN’s refugee agency show.
More than half of those escaping the violence have gone to Poland, where 2,336,799 refugees have been registered.
The Local Government Association (LGA) said some Ukrainian refugees have been “presenting as homeless”, despite being part of the UK Government resettlement schemes.
“One of the big issues we’re all worried about is people presenting as homeless," Chairman Councillor James Jamieson told MPs on the Levelling Up, Housing and Communities Committee.
“The LGA did a survey last week of councils – we had 190 responses from councils with housing responsibilities, which is about two-thirds of authorities, of which 57 of the 190 said they already had people presenting as homeless.
“That is 144 cases of homelessness – that’s 57 councils, 144 cases. I will make sure the data is correct and get that sent to you, but I’ll give it to you verbally.
“Forty-four of which were from the family scheme, 36 of which were from the sponsorship scheme and 64 were from unknown or other.
“We believe there is an element of people presenting as homeless because they are coming to Ireland and then, with the free movement, able to come to the UK, so that maybe an element of the unknown.”
Countries across the EU have adopted open-door policies while Britain retains a visa requirement on security grounds.
Initially, UK would only allow in Ukrainians who already had family in the country. It then introduced the Homes for Ukraine programme, where people offer their homes to refugees without familial ties.
Overall, 59,500 Ukrainians have sought entry into the UK, of which 28,300 have applied under the Homes for Ukraine Scheme and 31,200 under a separate Ukraine Family Scheme.