GMPDetectives 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”.
Investigators are “extremely concerned” for the welfare of the weeks-old baby and say locating the child is their “top priority”.
The Metropolitan Police said the family had arrived at the East Sussex 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 “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.”
Ms Marten’s father has previously appealed for her to come home, saying “find a way to turn yourself and your wee one into the police as soon as possible so you and he or she can be protected”.
Ms Marten has been estranged from her wealthy family for several years. She grew up in a stately home in Dorset which was used as a set for the 1996 film of Jane Austen’s Emma.
Police say the couple left their home in Eltham, south-east London, in September 2022 when Ms Marten began showing signs of pregnancy, and have since led a nomadic lifestyle.
They had been living an isolated life since starting a relationship in 2016.
Gordon has been registered as a sex offender in the UK since 2010 for a rape he committed aged 14.
He served a 20-year sentence in the United States before being deported to Britain.
An investigation began when their car was found on fire by the side of the M61 near Bolton on 5 January.
The occupants had left and police soon discovered that Miss Marten had given birth a day or two earlier without any medical assistance.
There have been several sightings since a missing person investigation was launched.
