A £10,000 reward is being offered in the search for the missing woman Constance Marten, her newborn baby and her partner, a convicted sex offender.
Marten, 35, and her 48-year-old boyfriend, Mark Gordon, who served 20 years in a US jail for rape and battery for an attack on a woman when he was 14, were last seen in East Sussex on 9 January.
The Metropolitan police believe the family are still in the UK and are likely to have been sleeping rough after buying camping equipment from a branch of Argos in east London on 7 January.
The force is offering a £10,000 reward to anyone who provides information that leads to them being found, adding: “Finding the baby is our top priority.”
DS Lewis Basford, who is leading the investigation, said: “We continue to be extremely concerned about the health and wellbeing of the newborn baby, which has had no medical care and has been on the move, and possibly exposed to sub-zero temperatures, for almost a month now.
“We’re also concerned for the welfare of Constance and Mark because our inquiries suggest that they were constantly moving and awake for at least a few days – which must be especially draining on someone who had recently given birth with no medical attention.”
Marten is from a wealthy aristocratic family with connections to the royal family and was a promising drama student before meeting Gordon in 2016. Since then, the couple have led an isolated life cut off from family and friends.
From about September last year, they began living in a series of Airbnbs around the country on short lets and amassed a significant amount of cash to enable them to live off-grid and avoid the attention of the authorities.
The couple are believed to have walked away from a car fire in Greater Manchester, in which most of their belongings were destroyed, and made their way to east London over the course of two days.
Whenever they have been seen on CCTV their faces are covered and the child hidden from view, although taxi drivers used by the couple in the first few days after they went missing said they had heard noises coming from a baby.