Johanita Dogbey, 31, was stabbed in broad daylight as she walked along Stockwell Park Walk near the O2 Academy Brixton on Bank Holiday Monday.
She was on the phone to her gran when the attack happened and was returning home for her mum’s birthday celebration after buying a present, the Evening Standard reported.
Emergency services were called to the scene just after 4pm, but she died at the scene.
A 33-year-old man was arrested on suspicion of murder yesterday.
Johanita’s brother Maurice told the MailOnline: ‘We are trying to understand what has happened and are completely broken.
‘As far as we know there was no link between my sister and the attacker. We are waiting to meet with the police to get a full update.
‘This whole thing has left us devastated. It’s too much for us.’
Initial inquiries from detectives at the Metropolitan Police suggest a man approached Johanita from behind before attacking her.
Officers said there is no information to suggest the killer and the victim were known to each other.
Detective Chief Superintendent Seb Adjei-Addoh, local policing commander for Lambeth, said: ‘This is a shocking attack and my thoughts are with the woman’s family and friends as they come to terms with this awful news.
‘We will do everything we can to support them at this incredibly difficult time.
‘I recognise the considerable concern this incident has caused and I’d like to reassure you that a dedicated team of detectives are carrying out a number of enquiries and have made an arrest.
‘Despite this, we have additional officers in the area to respond to any concerns from members of the community and I would ask people to report any suspicious activity to us.’