A £10,000 reward is being offered in the search for missing Dorset 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, grew up on the 5,000 acre Crichel Estate near Wimborne in Dorset.
She 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."
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