Dan Friend, one of the town’s councillors, said police had cordoned off a section of The Rope Walk, a path near the centre of the town.
On Sunday evening, officers could be seen standing at the ends of the path by the cordon, with a police van also seen in the town.
Officers from the Metropolitan Police also set up a tent and equipment in the Guildhall car park, on the western side of the cordon.
The cordon covers an area between New Street through to the Cow Leas Meadow area, Mr Friend said.
Residents in Sandwich have been asked not to gather at the scene.
Scotland Yard said police have routinely been searching areas of London and Kent as part of the investigation.
Serving police officer Wayne Couzens, 48, has been charged with Ms Everard’s kidnap and murder.