Three years ago Cambridgeshire County and Peterborough City councils were looking after just six children.
They are now responsible for 138 and are having to house them as far away as Nottingham. It is one of the biggest increases in the country.
Peterborough council said the rise was putting a "strain" on its services.
And both Peterborough and Cambridgeshire warn the numbers will rise to help ease pressures in Kent, where about 900 unaccompanied child migrants are currently housed.
Cathy Smith, first response and emergency duty officer at Cambridgeshire County Council, said the county council was only coping with the influx by using out-of-county placements more than 100 miles (160km) away.
"Social workers are often scouring the country trying to find placements for  these young people."
Wali, now 18, arrived on his own in the UK on the back of a lorry from Iran aged 17.
"I was living in Iran and I left because I was having some problems with smugglers who wanted me to work with them.
"I went to Turkey, Bulgaria, Serbia, Austria, Italy and then to France and then to England. There was no-one here for me.
"They gave us clothes and accommodation and I have gone to college. If they did not help we would be homeless people living in the street."
He said he was very grateful for the support he had been given by the authorities since arriving and said without it he would not have been able to cope.
Nicola Curly, assistant director of children's services at Peterborough City Council, said about one in 11 of its children in care was now a migrant.
"These are very traumatised young children," she said. "They have had long and difficult journeys and they need a lot of support when they arrive."
She added: "We have no option when a young person arrives.
"If they need accommodation and support then we have to provide that. It is starting to place a strain on our placement capacity. We are anticipating more children and young people. We have no idea how many."
The number of lone child asylum-seekers has risen 22-fold in Cambridgeshire, leaving local authorities struggling to cope, it has emerged.