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Medway Council says it cannot take on more asylum seeking children and is pursuing legal action against the government.
Council leader Alan Jarrett confirmed the authority is willing to go to the High Court after refusing to take on any more Unaccompanied Asylum Seeking Children (UASCs).
It has applied for leave to seek a judicial review, which can take place when the lawfulness of a public authority is challenged.
The move came after the Home Office sent instructions to all councils in November to take part in what's called the National Transfer Scheme, which had previously been something which they could take part in voluntarily.
Under the scheme, councils were asked to take on a quota of additional UASC to make sure they were not living in hotels and hostels. Medway's quota would have seen them taking on an extra 45 children.
The change in the rules about the National Transfer Scheme was welcomed by Kent County Council (KCC), which previously threatened legal action against the Home Office and twice had to raise the alarm to say it couldn't take on any more UASC.
Medway Council leader Cllr Alan Jarrett (Con) wrote to Kevin Foster, minister for safe and legal migration in December saying the authority was not in a position to accept any more UASC.
Cllr Jarrett argued the pressures on the council's childrens' services department should mean it should be exempt, but this was rejected by the government.
The authority was subject to scrutiny from a government-appointed inspector after the department received an "Inadequate" rating from Ofsted in 2019.
Since the report, the department has been subject to monitoring visits from the watchdog, with the most recent taking place in January.
The council is currently supporting 16 UASC who are aged over 18; there are less than five who are under this age.
However, there are another 28 UASC living in the towns who have been placed there by other local authorities.
Figures reported by the council towards the end of last year showed how the number of children requiring residential care placements had tripled since 2017 and the average cost of placements have increased by 60%.
Four years ago, the most expensive placement was £5,500 a week, but by 2020, this had increased to £10,520.
At the council's budget meeting earlier this year, the leadership confirmed an additional £6.1 million would be spent on the children’s services department, with its budget totalling just over £53 million.
Cllr Jarrett told the Local Democracy Reporting Service the number of UASC already allocated to Medway was likely due to its proximity to both Kent and the London Boroughs.
He said: "We have used up all our capacity, we're having to send some of our own children out of area at a huge increase in costs.
"Basically, Medway doesn't have the capacity and that's what we put to the government in the first place.
"The government's behaving completely unreasonably and that's why we are taking the steps we are.
"We have set out our case quite clearly. A Sixth Form maths student could see we don't have the capacity, but they have chosen to ignore that."
The Home Office was approached for comment.