A staggering 89,000 people in the UK signed up to host a refugee within the first day of the Homes for Ukraine site going live.
St Augustine's Centre in Halifax, which helps those forced to leave their home countries through no fault of their own, said it has already beginning to get calls from people in Calderdale who are keen to help.
He added it will be expanded with the support of charities, community groups and churches who can help with matching refugees to hosts.
A spokesperson for St Augustine's Centre said: "We welcome quick and effective efforts to find housing for people fleeing Ukraine, but we have concerns about the Homes for Ukraine scheme - namely that it fails to give those arriving refugee status, does not account for the complex emotional and mental needs of people fleeing war, and will not work quick enough to give the efficient response needed in this refugee crisis, amongst others.
"We continue to call on the Government for a commitment to a resettlement programme and changes to the Nationality and Borders Bill.
"We are already beginning to field calls from kind people in Calderdale offering their homes as places of refuge for people fleeing Ukraine. We are consulting with the council, Migration Yorkshire and the local Ukrainian community to ensure the appropriate support is available as we learn more.
"We ask anyone interested to contact Migration Yorkshire who are creating a database of people offering accommodation. You can email at [email protected] or call 0113 3788188.
"It is so important that we get this right - in the best, most effective way for both hosts and people fleeing Ukraine."
Those who have signed up to the scheme in Calderdale include former mayor of the borough and Calderdale Councillor Dot Foster and her husband Mick.
They have a spare room at their Pye Nest home - currently being used as Councillor Foster's office - which they are hoping to give to someone who has fled from the Russian invasion.
Mr Foster said: "You can't just sit there and observe. You've got to do stuff."
Councillor Foster added: "We've got a room that we could make available. It needs a bit of a clear out but it is do-able.
"I just think if we were in that position, I really hope that someone would offer to do that for us.
"If we can adapt out lives to help someone else, why wouldn't we?"
MP for Halifax Holly Lynch also has concerns about the Government's approach to helping Ukrainian refugees.
"The Government’s slow response to the refugee crisis has been incredibly distressing," she said.
"We have called for Home Office staff to be deployed at all the major travel centres on route for Ukrainian refugees so that we can undertake any necessary checks on the spot and issue Emergency visas without any unnecessary delays or journeys for already traumatised people.
"I welcome the sponsorship scheme which seeks to utilise the warmth and generosity of local people to open their homes to those who arrive, however it is entirely right that safeguarding remains a priority and that we learn lessons from past community sponsorship schemes which have moved at a glacial pace. We need urgency to this scheme."
MP for the Calder Valley Craig Whittaker has defended the Government and welcomed the new scheme.
He said: "The French Interior Minister recently said the UK has a ‘lack of humanity’ over the Ukrainian refugee crisis. This from a man and his President who stand by idly, watching tens of thousands of men, women and children being taken advantage of by people smugglers on the perilous journey across the channel, some to their deaths.
"This, however, isn’t a game of one-upmanship. It is a serious issue, not just for the refugees who are fleeing their homes, but for us too and our capacity to look after them when they are in the UK.
"Currently, we have over 80,000 refugees, most staying in hotels in this country. Many families are in one hotel room and often for well over 18 months. Some are here in Calderdale too with nowhere for them to move onto with homes at a premium and a huge backlog on healthcare.
"This is no way to treat the vulnerable, no matter where they come from, whether it be Afghanistan, Hong Kong, Ukraine or across the channel. It is also unsustainable.
"The UK is more than pulling our weight to help the overall crisis in Ukraine. We are the biggest European bi-lateral aid contributor to countries around Ukraine in supporting their refugee intake.
"We are giving more arms to Ukraine than any other European country, and the sanctions we have imposed are three times bigger in value than Europe combined, and bigger than America’s sanctions too.
"Those are the reasons why our approach to Ukrainian refugees is fair and balanced.
"Anyone in Ukraine who has family ties here in the UK can come here automatically with much of the criteria dropped for visas. In addition, we have the new sponsorship route, which guarantees a home here in the UK for potentially over 100,000 people.
"This is a much better way to treat refugees than sticking them in hotels with no hope for the short term or medium-term future.
"We should be proud of our approach and proud what we are doing to help Ukrainian refugees."