Campaigners say they have identified almost 400 refugee children living in the so-called Jungle camp in Calais who are eligible to come to the UK.
They handed the list to the Home Office and urged Home Secretary Amber Rudd to accept the children - many of whom reportedly have family in Britain.
Actress Juliet Stevenson told crowds outside that "history will judge us very harshly" unless the UK acts.
The Home Office said it already plans to transfer 150 children this year.
According to the campaign group Citizens UK, there are 800 unaccompanied children among some 7,000 refugees living in the Calais camp.
The group has drawn up a list of 387 who it says are eligible to be transferred to the UK.
A crowd of about 150 people gathered outside the Home Office in London to urge ministers to immediately bring over those stranded children.
Actresses including Stevenson, Vanessa Redgrave and Eastenders' Ann Mitchell, as well as religious leaders and local politicians, also attended the event.
They also paid tribute to three-year-old Syrian refugee Alan Kurdi, who drowned one year ago.
Stevenson, who starred in Truly Madly Deeply, said offering asylum to children was "a humanitarian issue that has been turned into a political one".
She said the "whole issue of immigration has become toxic and confused".
"Whatever you think about Brexit, or the EU, or the free movement of the workforce, that is a different thing to offering sanctuary to children fleeing war and violence," she added.
Redgrave said supporting the plight of vulnerable refugee children was a moral and civic duty and called for the government to agree to a special permit for refugees.
She said the UK government not only had "a moral duty, but a legal responsibility" to offer assistance.
Rabbi Laura Janner-Klausner, from the Reform Judaism movement, added: "We have their names, we know there are actually 387 of them.
"I've met some of them in Calais. Young, young children wandering around this refugee camp, who have a clear legal right to be here. And we should be letting them in today."
Campaigners say the children include 178 who have the right to come to the UK under an EU rule known as the Dublin III regulation because of their close family links in the country.
They say a further 209 are eligible under an immigration provision known as the Dubs Amendment.
The amendment to the Immigration Act, originally put forward by Lord Dubs, requires the government to arrange for the transfer to the UK and support of unaccompanied refugee children from Europe.
Lord Dubs, a Labour peer and long-time refugee campaigner, came to Britain as a child on the Kindertransport programme to escape Nazi persecution.
He has said: "I am deeply saddened that despite repeated calls from me and others, the government still seems to be dragging its feet on the commitments it made when the amendment in my name was accepted."
He called for Prime Minister Theresa May and the Home Office to take "immediate action".
Some of the children in Calais may be older teenagers, but should still be considered for asylum, he told BBC Radio 4's Today programme.
"Even 17-year-olds who've been traumatised by war and had their parents killed in front of them in, say, Syria, they're pretty vulnerable. They also need help."
He added: "Even the boys are pretty vulnerable. And they're liable to be taken into trafficking, into criminality and so on."
'Stretched to limit'
A Home Office spokeswoman commented on the campaigners' demands: "We are in active discussions with the UNHCR, other partner organisations and the Italian, Greek and French governments to strengthen and speed up mechanisms to identify, assess and transfer unaccompanied refugee children to the UK where this in their best interests."
The government was working "closely" with French officials to ensure children with family links in the UK are identified "without delay".
However, the Conservative council leader in Kent, Paul Carter, told the Today programme that resources in the county were already "stretched to the limit".
He said the council was looking after 1,500 young people aged under 18 who had arrived unaccompanied, costing between £40,000 and £50,000 "per young person".
Councillor Julian Bell, Labour leader of London's Ealing Borough Council, said earlier councils "stand ready to do our bit" but required co-operation from central government.