Lord Williams signed an open letter to Theresa May alongside the Right Rev Paul Butler, Bishop of Durham, the Right Rev David Walker, Bishop of Manchester, the Right Rev Peter Hill, Bishop of Barking, the Right Rev Adrian Newman, Bishop of Stepney and the Right Rev Christopher Chessun, Bishop of Southwark.
Other signatories to the letter include Muslim Council of Britain secretary general Harun Rashid Khan and Laura Janner-Klausner, the senior rabbi to the Movement of Reform Judaism.
September also saw more than 200 Christian, Muslim and Jewish clerics, alongside lead representatives of other faiths, sign an open letter urging Mrs May to unblock rules preventing refugee families being reunited in the UK.
The French president Francois Hollande has said the 'Jungle' migrant camp would close before winter, with its 9,000 inhabitants dispersed around the country.
The letter says the migrant children "have fled conflict and persecution, are now stuck in Northern France, deeply traumatised and at great risk as well documented by the anti-slavery commissioner you yourself appointed while Home Secretary".
It adds: "We are now just days away from the start of the full demolition of the Calais camp.
"None of us want the Calais 'Jungle' to exist. It is a stain on the conscience of both France and Britain.
"But in haste to clear it the need to protect children is even more paramount. During the last such demolition the charity Help Refugees documented that 129 children went missing.
"The time to act is now."
A Home Office spokeswoman said: "The clearance of the camp in Calais is a matter for the French authorities, who also have primary responsibility for unaccompanied children in France.
"The UK government has no jurisdiction to operate on French territory and can only contribute in ways agreed with the French authorities and in compliance with French and EU law.
"The UK has made crystal clear its commitment to resettle vulnerable children under the Immigration Act and ensure those with links to the UK are brought here using the Dublin Regulation.
"We are working continue to work with the French government and partner organisations to speed up mechanisms to identify, assess and transfer unaccompanied refugee children to the UK, where this is in their best interests."