Liberal Democrat Town Councillor Jim Pilling and his wife Catherine said: “Along with all of us, my wife and I have been watching in horror the unfolding situation in Ukraine.
“We decided that we would open our doors to up to four refugees, and go and collect them.
“But it seems that our Government will not allow us to do this.
"Visa are required, and only refugees with relatives living in the UK will be considered.
“We have asked several bodies including the Home Office and our MP David Morris to explain the exact requirements but, so far, we have not had any response.
"I am sure that we are not alone in being willing to offer the refugees a safe home and I am absolutely ashamed of our countries response to this growing crisis.
“All EU countries are allowing the refugees free entry to their countries if they can provide a passport, Poland in particularly has been superb with it's response, but our Government's reaction has been embarrassingly woeful.
"As of now (Sunday March 6) the UK has granted just 50 visas to the refugees. Around 1.5m Ukrainians have so far fled their country.
"It is reported today that 150 refugees were refused entry to the UK for lack of visas and turned back at Calais.
“Poland in contrast has accepted around one million refugees into it's country.
“We are not giving up on our wish to help the refugees who want to come to the UK, but we need clear guidance from the authorities to enable us to do this - or to tell us that we will not be allowed to help them."
David Morris MP said: “Town Councillor Pilling contacted me on Sunday afternoon to ask how he can host Ukrainian families in his home.
"The Government are currently in the process of setting up a humanitarian sponsorship pathway which will allow individuals, businesses and charities who want to help support displaced Ukrainians be matched with those requiring assistance who do not have family ties in the UK.
"Details of this new scheme will be released by the Home Office shortly.
“In the meantime, I have asked Cllr Pilling to register himself with the housing team at Lancaster City Council as they will be responsible for housing Ukrainians in the area on behalf of the Home Office.
“It is great to see that local people want to do what they can to help, and I want to thank all of the individuals and businesses who over the weekend have been fundraising to support the Ukrainian people.
"At the moment the most important thing is to ensure as many people as possible can get to safety in neighbouring countries and allow those with family in the UK to come here.
"In the coming weeks the focus will then change to enabling refuges in safe neighbouring countries to access the UK as we house these refugees across Europe.”