Notices have been posted in shops in the camp warning those in the camp will be evacuated from the area within two days, before the demolition of makeshift buildings in the shanty town.
The Right Reverend Trevor Willmott, the Bishop of Dover, said the situation in the Jungle was "intolerable".
The port city's police commissioner Patrick Visser-Bourdon (below, top) has visited the slum where legal notification of the order to leave the shops was posted in French.
Mr Visser-Bourdon said similar notices would go up once the French courts had given the go-ahead to clear the rest of the Jungle, where some 10,000 inhabitants are camped.
The death toll among migrants in Calais this year stands at 14.
The latest fatality was an Eritrean man killed after being struck by a vehicle driven by a Briton on the A16 motorway.
The Jungle closure plan will see 40 to 50 people being held at reception centres in regions across France for up to four months while authorities investigate their cases.
Those who do not seek asylum will be deported.
The Bishop of Dover said: "The human tragedy that is the Calais 'Jungle' camp has been a constant cause for concern and prayer in the diocese.
"Being but a few miles from our own coastline, its devastating impact on those that live and volunteer there, the local French community, lorry drivers and port workers, holiday-makers and security staff, has been impossible to ignore."
