Fourteen teenagers have arrived in the UK from Calais as a fast-track system was launched to transfer youngsters from the "Jungle" camp before it is demolished.
The Home Office confirmed a group of vulnerable children, aged 14 to 17, were transferred to Britain on Monday morning.
A spokesman for the department said: "This is the start of the process to transfer as many eligible children as possible before the start of the clearance, as the Home Secretary set out in Parliament."
The young people will be assessed and screened and may be cared for in specialist temporary accommodation for a short period before they are reunited with their loved ones, the Home Office said.
The arrival of the group, made up of youngsters who are said to originate from a variety of war-ravaged countries, including Syria and Sudan, has been welcomed by charities and faith leaders.
One man, who said his younger brother was among the refugees who had come over on Monday, spoke of his relief and joy at the prospect of being reunited with him after more than a decade.
Asif Khan, a 25-year-old chef who has been living in the UK for 11 years having fled Afghanistan, said his brother, Aimal Khan, 14, had been stranded in the Jungle for six months.
Speaking outside the Home Office building in Croydon he told the Press Association: "I really appreciate this. My brother was in Calais for the last six months.
"It was a blessing to receive him from there - I'm really happy.
"His journey was so difficult, it was by walking, by bus to Calais. He gets a new life now, because there are many people who died in Calais."
Dozens more children are expected to arrive this week after a team of British officials were sent to Calais to help French authorities speed up the transfer of minors ahead of the dismantling of the Jungle.
Campaigners including Citizens UK, which said it has reunited 60 children from Calais with relatives in Britain since March, claim to have identified hundreds of children in the camp who have a right to come to the UK – either because they have family ties here under the so-called Dublin regulations, or through the Dubs amendment.
Lord Dubs, whose amendment to the Immigration Act 2016 requires the Government to relocate unaccompanied refugee children from Europe, said: "In the coming days, Citizens UK's Safe Passage team will be working round the clock to ensure that all children with a legal right to sanctuary in the UK are brought to safety.
"This includes the children eligible under the Dubs amendment, for whom there is still no official process in place. No child must be left behind in the chaos of demolition."
He added: "Looking ahead we must never allow a repeat of Calais. The Government must learn lessons from this situation and realise that it has a duty to make the Dublin mechanism work across Europe, as well as establishing a clear procedure for children without family eligible for sanctuary under the Dubs amendment."
The actress Juliet Stevenson said it was a "proud moment" for Britain, adding that the country had done "the right thing".
Former Archbishop of Canterbury Dr Rowan Williams said he is "delighted" to welcome the children to the UK, but cautioned that this is the first step and more children need help urgently.
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He said: "We welcome the development. We do want to remind everyone, public and Government, that time is short.
"This is a matter of urgency and we want to see some progress not only on those children who already have the legal right to be here, but on those others who are covered by the Dubs amendment and whose needs can be considered by this country."
The Government has faced criticism over efforts to identify and transfer youngsters through the routes.
Last week Home Secretary Amber Rudd told the Commons that more than 80 unaccompanied children had been accepted for transfer under the Dublin regulation so far this year.
Under the rule, asylum claims must be made in the first safe country a person reaches – but children can have their application transferred to another country if they have family members living there.
The Home Secretary also said that more than 50 children had been taken, largely from Greece, under Lord Dubs' amendment to the Immigration Act.
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