The child is just three days old and was discovered lying on a pavement in an alleyway behind garages in Leyton, east London. Doctors who are caring for the baby at Whipps Cross Hospital in east London, dubbed him "Robert Alan" after the two ambulancemen who picked him up.
The infant, who is mixed race, was wrapped in a patterned shawl and dressed only in a pale green sleep suit. He still had a plastic yellow umbilical clip attached, which police believe has come from a local hospital or midwife.
They issued an urgent appeal for the mother to come forward or anyone who knew her to contact police.
Detective Inspector Phil Jones, of Leyton CID, said: "We are anxious to reunite the baby with its mother. I am particularly pleased that the baby has been found fit and healthy, and that's good news for the New Year.
"We have checked all hospitals in the area in a bid to trace the mother but to no avail. We believe the baby could have been born in a hospital or by a midwife at home as the clip used to tie the umbilical cord was a type only available to medical staff."
The baby, who weighs 7lb 11oz, was heard crying by a man on his way to buy a lottery ticket.
Dr Iain Macintosh of Whipps Cross Hospital said: "It could be that the baby was born in a hospital or by medical staff at home. The child was in good condition, he was relatively warm and had probably only been out in the cold for about half an hour. It seems he had been well cared for.
"It is vital that the baby's mother comes forward and I am worried about her mental state."
Mr Jones said: "This is a beautiful baby boy who needs his mum. Let us make this a happy New Year for both mother and child by reuniting them."Reuse content