Police questioning Constance Marten and Mark Gordon say they believe the baby whose remains were found in the woods may have been dead “for some time”.
They said there were “many unanswered questions” and have not yet been able to confirm the baby’s gender.
Ms Marten, 35, and Gordon, 48, were arrested on suspicion of gross negligence homicide and remain in custody.
The case has now been passed to the police watchdog.
No autopsy has yet been performed and the police have not formally established the child’s identity.
Ms Marten and Gordon – a convicted sex offender – were arrested in Brighton on Monday after a 53-day search, which began when their car was found on fire by the side of a motorway near Bolton on January 5.
The remains of a baby were found in the woods near where the couple were arrested on Wednesday, following a massive search involving hundreds of officers.
Metropolitan Police Detective Superintendent Lewis Basford said the case would be reviewed by the Independent Office for Police Conduct because the baby had died during the missing persons investigation.
Investigators need “time and space to establish more details about the circumstances of this tragic death”, he said.
He added that it was “too early to provide a specific date” for the baby’s death, and said investigators were “really devastated by this result”.
Police had an additional 36 hours to question the couple on Wednesday afternoon.
The search for the baby’s fingertips was carried out at near-freezing temperatures. It stretched east from Brighton to Newhaven, north of the town center into a nature reserve and beyond to the South Downs.
Witnesses told the BBC they saw teams rummaging through thick brambles, plots and bins, while locals had to watch out for anything unusual.
Officers were seen earlier Thursday searching the area near where the remains were found.
Police vans and a forensic tent were parked on a residential street near a wooded area popular with dog walkers that was closed as part of the investigation.
Ch Supt James Collis of Sussex Police said operations around Brighton would be reduced as the investigation had reached a ‘new phase’.
Floral tributes were left by locals, who police said had “overwhelmed” them with support and offers of help.
The disappearance of Ms Marten and Gordon has sparked a nationwide search and sightings have been reported in Liverpool, Essex and London, mostly limited to brief snippets of CCTV footage.
Police believe they were sleeping outside in a tent and living off-grid, sparking fears for the child’s health in wintry temperatures.
The last confirmed sighting of the pair before their arrest was in Newhaven on January 8. Their baby was with them and alive at the time, police said previously.
Ms. Marten comes from a privileged background and lived in a stately home growing up. She became estranged from her family in 2016 after meeting Gordon at drama school.