Detectives are appealing for information to help them piece together the events that led to a man sustaining a serious head injury.
Christopher Mapleston, 29, was found at approximately 03:00hrs on Sunday, 20 November lying on Arbuthnot Road, close to Pepys Road in New Cross. He had a laceration to his head.
He was taken by the London Ambulance Service to a south London hospital where doctors discovered that he had a fractured skull. He remains in a critical condition.
Due to his injury, Christopher has been unable to tell officers what happened that night.
Detectives from Lewisham CID are investigating and have established that Christopher had spent the night socialising with friends.
His friends last saw him running for a Route N343 bus close to Peckham Rye Railway Station between 01:30 and 02:00hrs. It is not known what happened between this time, and when he was found in the road less than two miles away.
Detective Constable Terry Martin, from Lewisham CID, said: "We cannot be certain whether Christopher's injury was the result of a fall or an attack. One line of inquiry is that he may have been the victim of a robbery as he was found without his Iphone 6.
"I would like to speak with anyone who saw Christopher between the railway station and Arbuthnot Road. He was wearing a distinctive green camouflage jacket.
"Have you found a mobile phone in this area of New Cross? Any piece of information, however small, will help us to discover what happened in the early hours of that morning."
Officers are keen to hear from anyone who saw Christopher that night. If it assists, he is described as white, approximately 5ft 7ins tall, of slim build with brown hair. He was wearing a green camouflage jacket, black trousers and trainers.
Anyone with information is asked to contact officers at Lewisham via 101.