Concern for missing aristocrat Constance Marten, her boyfriend Mark Gordon and their newborn baby continues to grow.

It is now believed they have been camping out in the Sussex countryside.

Over a month ago, the car the trio was travelling in was found on fire on the hard-shoulder of the M61.

READ MORE£10k reward to find missing aristocrat, partner and baby

They have been spotted since in east London, near East Ham and in Whitechapel Road on January 7.

Near midnight, they dumped a number of items, including a pushchair near Brick Lane. 

They got a taxi to Haringey early in the morning on January 8.

Constance, Mark and their baby were dropped off in another taxi in Newhaven in East Sussex at 4.56am just outside the entrance to the port.

They then walked to where the A259 crosses over the B2109.

They were seen sheltering from the rain, under the overpass, at about 6am.

At around 6.15am they walked along Cantercrow Hill into the fields beyond.

They were carrying a number of bags and their blue tent, and officers believe they have been camping in the area subsequently, although given the time that’s passed they could have moved on some considerable distance.

Det Supt Lewis Basford, of the Met’s East Area Command, said: "Previous appeals have resulted in around 300 calls from members of the public, but sadly they have not led to the couple and their baby being found.

"While we are very grateful to everyone who has already called, we still need to hear from anyone who has seen the couple since Sunday, January 8 and we are offering a reward of up to £10,000 for any information that leads to the family being found.

"I am appealing in particular to people who may have spent time in the countryside near Newhaven and elsewhere in Sussex to think carefully as to whether they may have seen Constance and Mark over the past four weeks.

"Given the time that's passed they may have travelled on, so I also need to hear from anyone who may have seen them further afield."

Addressing Constance and Mark directly, Det Supt Basford said: "Constance and Mark, your baby has spent the first month of its short life exposed to the elements when it should be safe and warm and, most importantly, seen by medics.

"After a month you must be running low on cash.

"Please pick up the phone and let us know, at the very least, that you are okay.

"We are ready to come to you and see that you and the baby get medical attention."

Det Supt Basford added: "For a month now Mark, Constance and her new-born have been continually on the move in sub-zero temperatures with no medical attention and we are increasingly concerned for their wellbeing.

"We know that the baby was still alive on January 8 and finding the baby remains our top priority.

"Maybe you have information but were reluctant to come forward 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 this highly vulnerable infant."

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

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