The woman, 42-year-old Naudel Turner, was coming home from her job as a health care worker when she was attacked by the man with a knife.
Police say the woman was a 'hard-working' mother of two boys, aged 19 and 20, from Fulham. She travelled to North London for her job.
It is not believed that Ms Turner knew her attacker, who stabbed the knife into his victim's chest before rolling a cigarette.
A witness to the event said: 'I head the screaming so I went over to see what was happening. I saw the woman lying on her back with neck wounds.
'There was blood everywhere. There was a man stood a few feet away from her against the railings.'
The witness added that the woman was still breathing when he arrived on the scene, but that the assailant just stood there and rolled a cigarette.
'She looked up at me, she took a breath, and shut her eyes. I was the last person she saw.'
'I was leaning over her and she was looking down, then she looked up at me, she took a breath, and shut her eyes. I was the last person she saw.'
Two men then apparently wrestled the man to the ground and held him down until Police arrived and arrested him. He is now remanded in custody.
Another witness claimed that the man had stabbed Ms Turner four times in the neck.
The incident happened just before 1pm yesterday in the Bruce Grove area of Tottenham. Police are appealing to anyone who may have been in the area at the time of the murder to come forward with information.