Kent County Council is facing a £6.1m shortfall in the costs of looking after vulnerable asylum-seeking children, blaming government under-funding.
A report says the financial hole covers the last two years and points out a series of factors that have left it without sufficient money to meet escalating costs.
Among them is the increasing number of small boats with groups of migrants trying to cross the channel from France, often organised by criminal gangs.
Social services chiefs say while the number of unaccompanied asylum seeking children - known as UASCs - is significantly down compared to what it was in 2015, there is evidence of a rising trend.
The report says 2018 saw 172 arrivals compared to 948 in 2015 but “it is of note there have already been 87 referrals between January and May 2019 compared to just 45 during the same period last year".
At present, the council looks after 267 UASCs and a further 895 who are classed as care leavers.
Kent County Council says one reason it is dealing with growing numbers of vulnerable children is the reluctance of other councils to participate in a government dispersal scheme.
The National Transfer Scheme (NATS) was set up to ease the pressure on authorities who deal with children arriving.
However, Kent has not participated in it since April last year - despite meeting the government’s threshold for doing so.
Social services chiefs say “there continues to be a significant delay in transferring young people through the scheme due to the fact it is voluntary".
Councils who had previously taken part in the scheme had similar concerns over Home Office funding.
One of the biggest pressures is attributed to a government requirement on councils to offer all care leavers support up to the age of 25.
Kent County Council's cabinet member for children's services Cllr Roger Gough said: "This has been a very long-standing issue and we have argued for many years that the support we get from the government for what we fundamentally believe is a national issue has not been adequate.
"We do have a shortfall but very recently we have seen some progress.
"That shortfall is due to come down partly because of a government review of UASC funding.
"The rates for 16-and-17-year olds have been increased and that means we should see a better picture.
"That said, the £6.1m is something we want to actively pursue.”
On the number of child asylum seekers increasing, he said some were being picked up in small boats carrying migrants who were crossing the Channel.
“It is not huge and way below what the figures were back in 2015," he added.
However, the report acknowledges the government has responded to some concerns, increasing the rate paid to councils for supporting 16-to-17-year-olds to the same for vulnerable children under the age of 16.
It has also recruited several specialist support staff who are being funded through the government’s Controlling Migration Fund.
Kent County Council has teamed up with other counties to press the government to set up four regional reception centres in the South East, one of which would be Ashford’s Millbank centre.
A Home Office spokesperson said: “We are very grateful for the support of local authorities like Kent County Council who look after unaccompanied asylum-seeking children.
"The Home Office provides funding to local authorities as a contribution to their support costs and recently increased the amount Kent County Council could claim as part of a significant wider increase in funding to support unaccompanied asylum-seeking children.
"The care of looked after children is also funded through the local government funding settlement.
"We are working with local authorities to help address the challenges they face when supporting unaccompanied asylum-seeking children who have turned 18 and are being supported as care leavers.”
The statement said that a review was also looking at the issue of funding for care leavers over the age of 18.