The London Borough of Bexley issued a notice that the road will be shut to all traffic from Monday, March 10.
The closure is to allow Cappagh Contractors, working on behalf of Thames Water, to fix a collapsed pipe.
This order is valid for 18 months, but the works are expected to be finished within 12 days.
During this period, no alternative routes will be provided.
The council said that access will be maintained for emergency service vehicles and for vehicles directly involved in the works.
The restrictions will only be in force when indicated by prescribed traffic signs.
The notice was issued by Andrew Bashford, head of highways, traffic, and infrastructure at the London Borough of Bexley.
Residents and businesses in the area are advised to plan accordingly for the duration of the closure.
The council has stated that the closure is necessary to ensure the safety of both the public and the workforce during the repair works.
The road will be closed for the entire length of Appleton Close.
The council has apologised for any inconvenience this may cause and thanked residents and businesses for their patience while the essential works are carried out.
For more information, residents and businesses are advised to contact Cappagh Contractors on 020 8947 4000.
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