A family hosting three people from Ukraine have been told they will not receive any money as part of the Homes for Ukraine scheme.
Karyna, her son and her mother were settled in East Sussex, but felt isolated living in a small village with limited public transport.
They are now living in Tunbridge Wells in Kent with Naomi Vallely's family.
However, Mrs Vallely has been told by Kent County Council they would not get any financial help.
Mrs Vallely said: "If we want to provide a nice comfortable home to the Ukrainians we need to have a little bit more money to be able to pay for the heating to be on."
"We don't at all want to say that they have to move out, but as the months go on, if the weather goes on being quite cold, it will become a little bit more difficult."
Karyna said her five-year-old son has been accepted in a Tunbridge Wells primary school.
"Now we live in big town… now we can go to the shops and we have many English friends and many Ukrainian friends," she said.
A Kent County Council spokesperson said: "We're very proud that Kent residents are generously hosting more Ukrainian families than any other county in the UK. But to manage pressures on local services – like schools, health care and housing – we are not able to accept guests who have been matched with hosts in other areas unless there are exceptional circumstances.
"We can't discuss individual cases but the approach Kent has taken is in line with central government guidance."
East Sussex County Council (ESCC) said it would only be able to continue to provide support if Karyna and her family were to move back to East Sussex.
"Government funding is only available to local authorities for host families living in their local authority area. This is due to the ongoing checks that need to be carried out to ensure refugee families are safe and receiving the most appropriate support", an ESCC spokeswoman said.
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