A £10,000 reward is being offered in the search for missing aristocrat Constance Marten, her newborn baby and her convicted sex offender partner.
The couple and their baby were last seen in Newhaven, East Sussex, on January 9, the Metropolitan Police said, but they believe the family are still in the UK.
They are believed to have been sleeping rough after buying camping equipment from a branch of Argos in east London on January 7.
Ms Marten, 35, and her partner Mark Gordon, 48, have lived an isolated life since they met in 2016.
Detective Superintendent 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 enquiries 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.
“Finding the baby is our top priority and we are now offering a £10,000 reward to anyone who provides information which leads to them being found.”
Constance Marten, 35, and her convicted sex offender boyfriend Mark Gordon, 48, were last seen on January 7 in east London after buying a tent and bedding.
Detectives fear for their baby’s safety in freezing temperatures and having received no medical attention since birth in early January.
Police said that Mr Gordon went into Argos on Whitechapel Road, east London, at 6.19pm on Saturday January 7 to buy camping gear including a blue two-person tent.
Mark Gordon, left, and Ms Marten (Metropolitan Police/PA)
The family then walked around the area for more than three hours, trying to flag down three black cabs who all refused to take them as passengers.
They were last seen walking along Brick Lane, towards Bethnal Green Road, at 10.01pm that night.
Detective Superintendent Lewis Basford, who is leading the investigation, said: “We are extremely concerned that a newborn baby – less than a week old at the time on January 7 – has been exposed to sub-freezing cold temperatures if Mark and Constance have been camping out somewhere as our evidence suggests.
“No child, especially a tiny, newborn baby, should be forced to endure such dangerous, potentially life-threatening conditions.
Mark Gordon bought a tent similar to this one (Met Police/PA)
“This is why it is absolutely vital that anyone with information about their whereabouts contacts us as a matter of urgency – whether it is with a recent or older sighting. Every piece of information is crucial to enabling us to find the baby and ensure it is OK.
“My officers will continue working tirelessly behind the scenes to piece together the family’s movements and current whereabouts. It could be that they are trying to blend in with homeless communities, either here in London or further afield, or they could be camping in more rural or wooded areas.
“They could be absolutely anywhere in the country. Please keep your eyes peeled, especially while you are out and about in waste ground or beauty spots, or while you’re walking the dog, and report any information, no matter how insignificant you think it is, to us.”
Ms Marten is from a wealthy aristocratic family with connections to the royals and was a promising drama student until she met Mr Gordon in 2016.
Since then the couple have led an isolated life cut off from family and friends.
From around September last year they began living in a series of AirBnBs around the country on short lets and amassed a significant about of cash to enable them to live off-grid and avoid the attention of the authorities.
Police began investigating their disappearance when officers were called to a car fire on the hard shoulder of the M61 near Farnworth, Bolton, Greater Manchester, on January 5.
The family were dropped off by a taxi on Whitechapel Road (Met Police/PA)
It emerged that the couple, who saw most of their belongings destroyed in the fire, walked away from the wrecked car before taking a taxi first to Liverpool, and from there to Harwich.
They then travelled again in a taxi to East Ham station on January 7 and were there between around 10.30am and 12.30pm, before later taking another taxi to Whitechapel Road at 6.14pm, being dropped off carrying an orange plastic bag and with a pram.
Whenever they have been seen on CCTV their faces are covered and the baby is hidden from view, although taxi drivers used by the couple in the first few days after they went missing heard noises from a baby.
Mr Gordon served 20 years in a US jail for rape and battery for an attack on a woman aged in her early 20s when he was 14.
Anyone who has information can call police on 020 7175 0785, or to remain anonymous contact Crimestoppers on 0800 555111 or online.
