Kent County Council (KCC) says it cannot safely look after any more child refugees, unless other local authorities step in to help.
It comes after a surge in people arriving in to the UK over summer, after making the journey across the Channel from France.
More than 400 unaccompanied asylum-seeking children (UASC) have made it to the Kent coast so far this year, according to Sky News analysis.
The council are asking for other local authorities across the UK to take in the children, to relieve Kent of the “impossible strain” that “has been placed on finite KCC social care resources such as social workers, independent reviewing officers, care workers, foster carers, accommodation and funding”.
“I am deeply disappointed and concerned that, despite our many efforts to avoid this unthinkable situation, it has been necessary to make this announcement today,” council leader Roger Gough said.
“This is a huge challenge for Kent, but a relatively small challenge to solve nationally, and should have been resolved before now.”
Mr Gough added that since 2014, the council has housed 1,500 UASC in Kent.
“The stark reality today is that, despite my conversations with the Home Office alerting them that Kent expected to reach safe capacity to meet its statutory duty of care this weekend, 13 new arrivals in the last two days has now tipped the balance and the council simply cannot safely accommodate any more new arrivals at this time.”
Sue Chandler, Cabinet member for Integrated Children’s Services in Kent, added: “KCC will continue to review the situation and stay in contact with the Home Office and other UK local authorities for support.
“If every other local authority in the UK were to immediately accept two or three (under 18 year-old) UASC from Kent into their care, Kent’s numbers would reduce to the council’s safe allocation as stated in the National Transfer Scheme (231 children) – Kent is currently caring for almost triple this amount.
A Home Office spokesperson said: “This is an unprecedented situation and we have been working incredibly closely with Kent county council to urgently address their concerns.
“We continue to provide Kent county council with a high level of support, such as significantly increasing funding and reducing pressure on their services through a national transfer scheme.
“We are also providing extra support with children’s services and we continue to work across the local government network on their provision for unaccompanied minors.”