The children are understood to have left the port in northern France on Monday morning and will be reunited with relatives who are already in Britain. Upon arrival they will register with the Home Office in Croydon, south London.
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 camp.
Charity Citizens UK welcomed the arrival of the group on Monday, saying it has reunited 60 children from Calais with relatives in Britain since March.
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.
"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."
Campaigners say they 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.
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 regulations 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.