A £10,000 reward is being offered in the hunt for aristocrat Constance Marten, who went missing weeks ago with her newborn baby and partner.

The 35-year-old, who is from a wealthy family with connections to the royals, was last seen with her boyfriend Mark Gordon, 48, and their child on January 8.

The trio's car was found on fire on the M61 near Bolton more than three weeks ago but the occupants were not at the scene.

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Constance had recently given birth, possibly one or two days before, and neither her nor the baby had been assessed by medical professionals, said the Met.

The Met revealed details of the reward and of the latest sighting of the family in Newhaven, East Sussex, on Sunday, January 8.

Investigators say they took a taxi from Haringey in north London shortly before 1.30am and were dropped at the entrance to the port at 4.56am.

Police do not believe they took a ferry and instead remain somewhere in the UK.

The baby was alive but detectives are concerned for its welfare.

Det Supt Lewis Basford 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.

"Maybe you have been reluctant to come forward before, for whatever reason, with key information to help us find the family.

"It does not matter why you did not speak to us earlier, what matters is doing the right thing now for the good of a vulnerable newborn baby.

"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."

Det Supt Basford added: "We know they were still in possession of camping equipment on Sunday, January 8 and so I’d encourage people to remain vigilant and keep a look out for a blue tent.

"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 to us."

Anyone who has information on the family’s whereabouts is asked to call the incident room on 020 7175 0785.

Alternatively, information can be reported anonymously to the independent charity Crimestoppers on 0800 555 111.

Reporting by PA.