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Kent County Council says it is optimistic the Government is preparing to settle its claim to be repaid money it has spent looking after child asylum seekers.
It follows a top-level summit of council chiefs and an earlier meeting with two key ministers on Tuesday.
KCC said ministers indicated they were prepared to resolve a funding crisis that has left the council owed £8million in backdated grants.
By law councils must provide care and support to the children but because government grants often do not cover the real costs many say they are out of pocket.
KCC leader Paul Carter (Con) said: "We desperately need a long-term solution to this national issue, so we do not have the same situation every year, where the costs of supporting the children fall to taxpayers living in the most affected areas."
But he warned that KCC was determined to ensure what it called historic debt owing chiefly from the Department for Children, Families and Schools was also repaid.
In a statement, the Department for Children, Schools and Families, said: "All sums to which Kent are entitled under the the care grant programme have either been paid or are in the process of being paid.
"However, we recognise local authorities still consider there are outstanding issues about funding services for this group of vulnerable young children."
A Home Office spokesman said: "We believe that our immigration system needs to be compassionate and sensitive to the needs of children and victims of trafficking. That’s why we’re studiously fair in the extra cash we give councils to help look after children who claim asylum.
"We’ve also proposed new plans for specialist councils to improve care and combat trafficking."