The couple left the car on foot and are believed to have first travelled to Liverpool.
There were other sightings of them in Harwich and Colchester in Essex in the following days, and a CCTV image released previously is thought to show Ms Marten in a red shawl near Harwich Port.
Police said on Thursday that the latest sighting was on Saturday 7 January, when they took a taxi from Harwich to East Ham station in east London.
CCTV footage recorded them there between 11.45am and 12.30pm.
Detective Superintendent Lewis Basford, from the Metropolitan Police, appealed for the pair to urgently get in touch so they can check the baby’s health.
“Being on the move for a week must be exhausting for new parents and a newborn baby,” he said.
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“Constance and Mark, I appeal directly to you, please think of your baby’s health and wellbeing and get in touch with us so we can ensure your child is medically well and has no underlying issues.
“Please do this for your child. You wouldn’t be able to forgive yourself if they became poorly. All we want to do is help you and your baby.”