Constance Marten is thought to be sleeping rough with her newborn and convicted sex offender partner.
Detectives are offering a £10,000 reward in the search for Constance Marten, her partner and newborn baby.
Police believe the 35-year-old is sleeping rough with her child and Mark Gordon, 48, a convicted sex offender.
The family were last seen in Newhaven, East Sussex, three weeks ago and are thought to be using camping equipment to live off grid.
Police fear the baby has been “exposed to sub-zero temperatures”.
The Metropolitan Police said the family had arrived at the port by taxi just before 05:00 GMT on 8 January, but officers believed they were still in the UK.
They were seen carrying a blue two-man tent, sleeping bags and pillows they had purchased from Argos the previous evening.
Police added that “the baby was alive and with them when they got the taxi to Newhaven”.
Det Supt Basford appealed for information from anyone who might be helping the couple to come forward, saying “it does not matter why you did not speak to us earlier”.
He continued: “Maybe you saw them wandering the streets? Perhaps they asked you for directions? Maybe they got into your taxi, or they came into your establishment to buy food and drink?
“Please contact us with any information you have, because every single bit of information we get will assist us with finding them.
“I’d like to stress that if you have taken cash to provide a service to the family, whether that’s giving them a lift, accommodation or something else, that you are not in any sort of trouble, we just need to hear from you.”
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