The process for resettling Ukrainian refugees in the UK has not been “as seamless as it should have been”, the minister in charge has admitted.

Lord Harrington, who was made a peer and appointed minister for refugees by the Prime Minister following criticism of the UK’s Ukrainian refugee response, said the visa application process for those fleeing the war in eastern Europe was taking too long.

But the Conservative peer told MPs that staff were working evening and weekends in a bid to speed up the process.

A little under 60,000 applications have been received for both the Ukraine Family Scheme, where refugees can apply to be reunited with relatives already living in the UK, and the Homes for Ukraine sponsorship scheme, which allows individuals and other groups to offer accommodation to those wanting to travel to Britain.

The Home Office confirmed on Wednesday that, as of March 29, the total number of visas issued was 25,500 – including 2,700 under the sponsorship scheme and 22,800 under the family scheme.

Speaking to the Levelling Up, Housing and Communities Committee, Lord Harrington said: “If I’m positive, I can say we’ve got 30,000 completed forms thereabouts.

“But we have not got everything right. It is not as seamless as it should be.”

He added: “We (the Home Office) are not trying to slow things up. The last time we looked, there were more than 300 staff and if we include both schemes, about 500 staff.

“We’ve started evening working, we’ve started weekend working.

“This is like an emergency operation.

“It is not that, ‘Oh they will just have to wait’ – it is people there who are desperate to come over, they’ve got through the system and we’ve got to get them here as quickly as possible.”

Asked how many people had arrived as part of the Homes for Ukraine scheme, the former Watford MP said it was “too early to publish that data” but vowed to write to the committee by early next week with the figures.

He said he hoped civil servants would be able to process 15,000 applications per week via both schemes within the next three weeks.

Lord Harrington – who was previously involved in the Syrian resettlement scheme – said there was a need for security checks to ensure Ukrainians applying “are who they say they are”, but that questions such as “are you a war criminal?” had been removed from the standard form that had been used.

“There has been some talk, quite correctly in my view, that the visa application process, the actual filling it out, is too slow,” Lord Harrington added.

“I agree with that. I sat down on Saturday morning and spent just under an hour filling one out myself, and I was sitting comfortably with a cup of tea rather than being a refugee, not in the Ukraine but in Poland or wherever.

“We are going through every step of trying to shorten that form.”

Emma Haddad, director general for asylum and protection at the Department for Levelling Up, Housing and Communities (DLUHC), said the length of the form for the sponsorship scheme had been cut by a third since applications for refugees first opened after the conflict with Russia started.

Earlier in the session, MPs heard how some Ukrainian refugees have been “presenting as homeless”, despite being part of the UK Government resettlement schemes.

Councillor James Jamieson, chairman of the Local Government Association (LGA), said it was an issue councils were “all worried about”.

He told the committee that 144 Ukrainian arrivals had declared themselves homeless to 57 councils.

“Forty-four of which were from the family scheme, 36 of which were from the sponsorship scheme and 64 were from unknown or other,” Mr Jamieson added.

“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 (is) maybe an element of the unknown.”

DLUHC officials said they would be working with councils to understand the “scale” of the problem and that local authorities would be able to fund accommodation out of their individual refugee grants.

More than four million people have fled Ukraine since the fighting started on February 24, according to the UN refugee agency.