The victim, a woman in her 20s, was on Lordship Lane at 4.45pm on August 25 when she was approached by a man.
He swore at her, hit her in the face and then left before police arrived.
The woman was treated by paramedics at the scene before being taken to hospital.
Met Police detectives are now appealing for the public’s help in identifying the attacker.
He is described as a Black man with balding hair in his 30s or 40s who was wearing dark clothing.
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Detective Constable Charlotte Kerr said: “We are working hard to find the person we believe is responsible for this senseless and unprovoked attack.
“While we continue our enquiries, we hope our increased neighbourhood police presence will offer some reassurance to women and girls throughout the local area.
“If you saw anything on Monday, August 25 – particularly between the junction of Lordship Lane and Chesterfield Grove at around 4.45pm – do not hesitate to get in touch with us.
“No matter how small you think your information is, it may be the key that unlocks our investigation.”
Anyone who can help identify the suspect is asked to please contact the Met via 101, quoting 5018/25AUG or 01/7897951/25.