For the A-list actor, it is a return trip to the Towns where he filmed Sherlock Holmes and its sequel at Chatham's Historic Dockyard.
Law has been shooting the thriller Black Sea - much of which is set on Black Widow, a 60s-built Soviet sub more used to patrolling the Baltic Sea.
The crew and cast have been seen embarking on a chartered launch on Rochester's Esplanade early in the morning to reach the vessel just the other side of the bridge.
About a dozen caravans and a white-painted bus, thought to be used for catering, have taken over the council coach park in Gas House Road, Rochester.
Sightings of 40-year-old Law have been few and far between.
Mother Maria Rayner believes she spotted him on a boat when she was with her daughter in the play area in Canal Road, Strood.
She saw a man wearing a white hat on boat leaving the submarine and - on taking a closer look - was convinced it was Law.
The submarine where the film is being shot
Maria said: "He was surrounded by a lot of people. We were quite far away, but me and my husband both recognised him. The boat went towards Rochester Bridge and then went under the bridge and disappeared from our view.
"It was quite exciting - it's not every day you see Jude Law go past on a boat."
Pete Kray, manager of The Crown pub in Rochester, believes he might have spotted him having an early-morning cigarette near the riverside pier.
Submarine owner John Sutton has been on the scene most days since the crew arrived at the beginning of last week.
Cabins and equipment on a barge near the sub
Black Sea is the second movie to be filmed on the sub. The Fitzroy, a black comedy was shot there last year.
Mr Sutton said: "I am looking forward to seeing both films."
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