Kent County Council (KCC) is caring for 720 unaccompanied children who have crossed the English Channel to Dover - up from 630 at the start of August.
The council is to reopen Appledore former reception centre near Cranbook to house about 40 boys aged 16 or 17.
It is also converting a disused care home in Whitstable for under 18s.
It comes as the Conservative MP for Tonbridge, Edenbridge and Malling added his voice to calls for the government to do more to help refugees and migrants entering Europe.
Tom Tugendhat tweeted: "Our common humanity, demands action at home and abroad."
The Red Cross, which works with young migrants in Kent, said the "overwhelming majority" who arrived in Dover from migrant camps in Calais claimed asylum.
"I believe the numbers are around 95%," said spokesman Rhys Cutler.
Children under 14 who arrive in the UK alone are taken into foster care while older teenagers live in the community as cared-for children.
David Slater, chaplain for Eurotunnel and the Port of Dover said some young asylum seekers arrived in Calais after "absolutely horrendous" journeys.
"In some cases they are running away from wars, but frequently they are being sent by their family who have clubbed together to get the money to send them because they will then be potentially earning in Europe," he said.
"These are children who have got an awful lot of pressure on them."
In July, KCC announced it was to convert the disused Ladesfield Care Home in Whitstable to house young migrants.
Now it has said it will also bring back into use the Appledore building at Swattenden outdoor education centre to help ease pressure on its children's services.
"We need extra capacity as it is not possible to predict the number of unaccompanied asylum-seeking children who will arrive at the border in need of our care," said Councillor Peter Oakford.
"Since June this year there has been an unprecedented increase in the number of arrivals.
"We have accommodated as many as is possible in our existing provision at Ashford but it reached full capacity several weeks ago."
They say a picture is worth 1,000 words and the picture of a Syrian child's body washed up on the beach in Turkey seems to have galvanised the debate over whether the UK should take more asylum seekers.
Even Conservative MPs have stepped up the pressure on the government. The MP for Tonbridge and Malling Tom Tugendhat took to Twitter to say that he'd "spoken to many in West Kent who want us to do more" and he agreed with them.  He also said our common humanity demands action at home and abroad.
The government's line has always been that they are at the forefront of the response to the Syrian crisis, but after growing calls for Britain to do more, the Prime Minister has now said that he felt deeply moved by the sight of that young boy on a beach in Turkey.
He said "Britain is a moral nation and we will fulfil our moral responsibilities" but he has stopped short of any commitments to taking refugees.
A former reception centre for asylum-seeker children is being brought back into use following an "unprecedented" surge in the number of young migrants.