In a press briefing this evening Detective Superintendent Lewis Basford from the Metropolitan Police confirmed search teams had found the body near Stanmer Villas in Brighton.
Marten, 35, and Gordon, 48, remain in custody after being arrested on Monday night on suspicion of child neglect and then later of gross negligence manslaughter.
In a statement Detective Superintendent Lewis Basford from the Metropolitan Police said: “It is my very sad duty to update you that this afternoon officers searching a wooded area close to where Constance and Mark Gordon were arrested discovered the remains of a baby.
“A postmortem will be held in due course, a crime scene is in place and work at the location is expected to continue for some time.
“This is an outcome that myself and the many officers who have been part of this search had hoped would not happen.
“I recognise the impact this news will have on the many people who have followed this story closely and can assure them that we will do everything we can to establish what has happened.
“Constance Marten and Mark Gordon remain in custody after an application for the extension of their detention for a further 36 hours was sought and granted by Brighton Magistrates Court.
“It is imperative now that the media and members of the public refrain from speculation and comments online that could be prejudicial to the potential court proceedings.
“No further information about the discovery will be shared at this time.
“I ask again that anyone with information that could support the investigation should call the investigation room.
“I’d like to thank the media, the public and our colleagues in Sussex for their continued support.”
Chief Superintendent James Collis from Sussex Police said: “I would first and foremost like to extend my heartfelt condolences on behalf of Sussex Police to the wider family of the baby at this time.
“I understand that the conclusion of this search will be heart-breaking for the community and the wider public who have been impacted by and have been so supportive of this search and the investigation from the outset.
“I would like to thank the public including the member of public whose information led to the arrests, the huge number of people who came forward with information and to those who volunteered to assist with the searches.
“We continue to support the Metropolitan Police as they conduct their investigation and the wider community as we come to terms with this tragedy.”
The news comes after a desperate search involving more than 200 officers since the pair were arrested.
Hundreds of police officers and search and rescue experts scoured 90 square miles of the Sussex countryside in a bid to find the baby, who had not had any medical attention since being born in or near a car in Bolton on January 5.
Metropolitan and Sussex police used helicopters, sniffer dogs, thermal imaging cameras and drones.
Marten, who comes from an aristocratic family with royal connections, first went missing with boyfriend Gordon, when their car was found abandoned and on fire at the edge of the M61 on January 5.
From there they travelled around the country by taxi, avoiding police by paying for everything in cash, covering their faces while on CCTV and moving locations frequently, often after dark.
They were finally arrested minutes after a member of the public tipped off police, but their baby was not with them.