The scheme opened on March 14, with the aim of allowing individuals, charities, community groups and businesses to bring Ukrainians – including those with no family ties to the UK – to safety.
However, Britain retains a visa requirement on security grounds while other European countries have waived checks in response to the humanitarian crisis caused by the Russian invasion.
The total number of applications from Ukrainians wanting to come to the UK was 59,500 as of March 29, the Home Office said.
This includes 28,300 under the Homes for Ukraine Scheme and 31,200 under the separate Ukraine Family Scheme, which allows Ukrainians to join relatives living in the UK.
There have been 25,500 visas issued altogether, including 2,700 under the sponsorship scheme and 22,800 under the family scheme.
The Local Government Association (LGA) said some Ukrainian refugees have been “presenting as homeless”, despite being part of the UK Government resettlement schemes.
Chairman Councillor James Jamieson told MPs on the Levelling Up, Housing and Communities Committee: “One of the big issues we’re all worried about is people presenting as homeless.
“The LGA did a survey last week of councils – we had 190 responses from councils with housing responsibilities, which is around 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.”
Deputy Prime Minister Dominic Raab has warned that Russia’s announcement that it is scaling back operations around the Ukrainian capital, Kyiv, should be treated with caution.
The Russians said the move was intended to “increase mutual trust” in face-to-face peace talks which resumed in Istanbul on Tuesday.