More than 60 Jewish and Christian leaders have written a letter published in The Times which calls upon French authorities to postpone dismantling the northern section of the site until the youngsters are safe.
In the letter, they say: "We are deeply concerned to learn that French police are planning to demolish the northern area of the Calais "Jungle" camp.
"[We] are calling on the authorities to stop the demolitions until all the children with a full legal right to be in the UK have been transferred and the remaining children have been safeguarded.
"Theresa May has seen this situation develop as home secretary. It would be admirable if one of her first acts as prime minister was to show the moral leadership this desperate situation demands."
One of the signatories, The Bishop of Southwark Rt Revd Christopher Chessun told Premier's News Hour: "Before any demolition takes place, provisions should be made for the well-being of children.
"We should initiate action - our governments, we hope, will be encouraged by us - to ensure that this happens."
The bishop also had this message for the authorities in France, saying: "Take enormous care before you take action to consider the lives and well-being or vulnerable people, some with the most terrible stories to tell of what they have endured and suffered elsewhere.
"We should also have gratitude for the French authorities and the Calais authorities for the way they have coped with an extremely difficult situation."
The right-wing Mayor of Calais, Natacha Bouchart, has been quoted as saying the destruction of the camp has been approved by the French interior minister Bernard Cazeneuve.
Natacha Bouchart said: "We can't wait any longer. We need to know as fast as possible when and how the Jungle will be torn down."
There are more than 600 unaccompanied refugee children in the so-called "Jungle" camp, 300 of whom are eligible for protection in the UK, Citizens UK believes.
The organisation, which help produced the letter in The Times, says clearing the southern area of the camp earlier this year left many children unaccounted for.
It is also warning the outcome of dismantling the northern area is likely to be even worse because no extra accommodation has been made available.
Among the signatories are the Bishop of Southwark Rt Revd Christopher Chessun, the Bishop of Durham Rt Revd Paul and the Bishop of Manchester Rt Revd David Walker.
The Bishop of Croydon Rt Revd Jonathan Clark, the Bishop of Barking Rt Revd Peter Hill, the Bishop of Dover Rt Revd Trevor Wilmot and Rt Revd David Hamid from Diocese in Europe have all supported the document.