They come amid criticism that the Government is not granting visas fast enough, leaving families and sponsors in limbo.
The Ukraine Sponsorship Scheme, also known as Homes for Ukraine, allows people to volunteer to house refugees.
Sponsors offer accommodation for at least six months, with those receiving sponsorship allowed to live, work and study in the UK three years.
Across the UK, 51,300 visas had been issued by April 27, equating to around 69 per cent of the 74,700 applications made.
The proportion of people waiting has dropped since April 7, when just 12,500 had been issued from 43,600 applications.
But the number of Ukrainians that have come to the UK through the scheme remains low, with the latest national figures showing just 11,100 had arrived by April 25.
The Government cautioned the data is likely to contain some duplicate records, while around two per cent of sponsors could not be assigned to a local area.
Some warn that delays in processing are impacting the number of refugees arriving in the UK, with reports of families unable to travel due to individual members not having visas.
Stephen Kinnock, shadow minister for immigration, said it was “truly inspiring” to see so many households open their doors to refugees.
But he also criticised the Government’s handling of the scheme, saying issues with processing visas had created a “bureaucratic nightmare”.
Refugees have also been arriving through the Ukraine Family Scheme, which allows Ukrainian nationals to join relatives in the UK.
As of April 27, 34,900 visas have been provided under the scheme nationally, of which 16,000 people had arrived by April 25. Local data is not yet available.
A Government spokesperson said: “The changes the Home Office has made to streamline the visa system, including simplifying the forms and boosting staff numbers, are working and we are now processing visas as quickly as they come in – enabling thousands more Ukrainians to come through our uncapped routes.”