He also set a target of bringing in 15,000 people a week, after the UK Government faced heavy criticism for the slow pace of its refugee scheme.
But more than two weeks after it was launched less than 5,000 refugees have arrived in Britain under scheme, despite over 200,000 individuals and organisations offering up their homes to Ukrainians.
And it was revealed on Sunday that Ukrainian refugees who travelled to Scotland after fleeing their war-torn homeland had been forced to present to local authorities, including Glasgow City Council, as homeless after arrangements with their planned hosts broke down.
Lord Harrington acknowledged the process had been “far too slow”, blaming systems ill-equipped to cope with processing the mass influx of applications.
“We did not have and we’ve never had a proper system of administering the mass flow of people from abroad,” he told the Sunday Times.
“The asylum system, the Syrian refugee programme, and everything else was based on a much smaller volume of people.”
The former Tory MP, who has offered to use the scheme to house a Ukrainian family at his London flat, said people were working around the clock to speed up the procedure.
He acknowledged the process “is not as automated as it should be” and appeared to hit out at the Home Office for taking “far too long” to carry out checks on the refugees and their UK sponsors.
Lord Harrington is now working with home secretary Priti Patel to reduce the mandatory 51-page application form, which includes questions such as: “Are you a war criminal?”
“I want to get this process down to a reasonable amount of time,” he said.
“I am happy to say publicly that my target is 48 hours from when they download the application form to when they are given permission to travel.”
It comes as the Department for Levelling Up Housing and Communities announced welcome hubs across airports, ports and train stations will be set up to welcome Ukrainian refugees.
Hubs are already up and running at airports such as Luton, Gatwick, Stansted, Birmingham, Manchester, and at London’s St Pancras International train station.
Nearly £2 million is to be spent on 31 hubs across 27 local authorities.
More than four million Ukrainians have fled their country since Russia invaded in February, the vast majority settling in Poland, according to the UN refugee agency UNHCR.
About 6.5 million people have been displaced within Ukraine.
Labour’s Jonathan Reynolds said the UK had “not yet met the scale of the challenge” in taking in Ukrainian refugees, when compared with other Nato countries.
The shadow business secretary told Sky News: “There’s been a huge response from the British people around this … people signing into the Homes for Ukraine scheme, the worry is how is that feeding through on the ground?
“I almost think we’re struggling to understand the sheer scale of this – I mean, the figures of people [refugee intake] in Poland and Romania alone.
“These are levels of movements of people in Europe that we just haven’t seen for decades.
“And I think when you see what other countries are coping with, and doing, it’s hard to say that as of yet we have met the scale of that challenge.”
North of the Border, a number of refugees have contacted Glasgow City Council to say they are homeless since arriving, with some believed to have come under the Homes for Ukraine scheme.
Reasons for being unable to stay with host families have included HMO licence restrictions, which limit the number of people allowed to live in a rented property.
Scottish Labour local government spokesperson Mark Griffin said: “A safe, secure and comfortable place to stay is the very least we owe those fleeing the war in Ukraine and seeking refuge here.
“The SNP must make sure that every council in Scotland has the resources they need to deliver any the necessary accommodation and services, and help refugees settle.
“We cannot let years of cuts to local councils compromise our response to this crisis.
“Both the Scottish and UK governments must work together to ensure the host scheme is fit for purpose, by speeding up visa applications and putting the proper safeguards in place.”
Gary Christie, head of policy, communications and communities at the Scottish Refugee Council, had earlier said: “Undoubtedly we will see private sponsorship offers not work out or families not able to accommodate their loved ones they are so desperate to bring to safety. It’s essential they are offered whatever support they need to feel safe and welcome in Scotland.”
A UK Government spokesperson said: “Everyone coming to the UK under the Homes for Ukraine and Ukraine Family Scheme will have access to healthcare, education, benefits and job support on the same footing as UK nationals.“These schemes are designed to ensure people who are coming to the UK fleeing the Russian invasion are provided with accommodation by their family or sponsor, and are only open to those applying from outside of the UK.”