Detective Inspector Ian Baker, leading the inquiry, said: 'Baby Harry is doing well under the care of hospital staff but we are very worried about his mother.
"If you see this appeal, please come forward and let us know you are safe.
"I know you must be feeling very frightened and alone to have done what you did but please make contact with us or your local hospital or GP surgery so they can check you are OK and offer you medical care and support.
"Little Harry needs to be reunited with his mother so we would urge anyone else with information, or who saw anything out of the ordinary in the Balaam Street area on Sunday morning, to please come forward." Anyone who can help is asked to call police on 020 8217 6528 or via 101.
Staff looking after him are calling him Harry until his true identity comes to light.
Meanwhile officers and doctors are urging his mother to come forward and get her own medical support.
In a direct appeal to the child's mother, the officer leading the inquiry, DCI Jim Foley, said: 'We are growing increasingly concerned for your welfare and I would urge you to make contact with us or your local hospital or GP surgery.
It is really important that we know you are safe.
"I would also ask that anyone who has information that could help us to reunite this baby with his mother to come forward."