Polish national Ania Jedrkowiak died at the scene of the attack on Tuesday.
Separately, detectives have arrested a 29 year-old man on suspicion of murder - this arrest has been descibred by those close to the investigation as “very significant”.
The killing sent shockwaves through the local community in south Ealing - this is what we know so far.
Who was the woman?
The woman has been named locally as 21 year-old Polish national, Ania Jedrkowiak.
Ms. Jedrkowiak was found in an alleyway just off Church Gardens in south Ealing.
Paramedics attempted to save Ms. Jedrkowiak’s life but she was pronounced dead at the scene.
Are the Met treating the death as murder?
Yes. The Met has confirmed they are treating the death of the woman as murder.
The murder investigation was launched soon after the woman’s body was discovered in the alleyway.
“Police were called at 00:10hrs on Tuesday, 17 May to reports of a stabbing in an alleyway off Church Gardens, South Ealing.
“Officers attended along with London Ambulance Service and London's Air Ambulance,” confirmed the Met.
The Met added: “A 21-year-old woman was found to have suffered a number of stab injuries.
“Despite the best efforts of emergency services, she was pronounced dead at the scene. Officers are confident they know the woman's identity and are in the process of informing her next of kin.”
Did the Met say anything else?
West Area BCU Commander Sean Wilson who is responsible for policing in Ealing said:
“This is a truly shocking incident which will understandably cause significant concern among the local community and Londoners as a whole.
“Violence of any kind, but particularly against women and girls, has a profound impact on communities and this will understandably impact on the confidence of those in the area going about their daily business.
“I want to reassure the Ealing community that a team of specialist homicide detectives have commenced an investigation and they will use their skills and experience to ensure that whoever is responsible is brought to justice.
“My local officers will also be in and around the area in South Ealing; if you have any concerns I would encourage you to approach them and speak to them. You can also speak to your local neighbourhood policing team or dial 101.”
A crime scene remains in place and enquiries are ongoing.
Anyone with information about the incident is asked to call 101 or tweet @MetCC quoting CAD 77/17May. To remain anonymous contact Crimestoppers on 0800 555 111.
How has the community responded?
One neighbour said: “Yeah it’s pretty shocking. I heard a commotion this morning, sirens and lots of shouting. It woke me up.”
Another local resident said: “It is pretty scary, considering it happened so close to a school.”
A local primary school had to close because of what happened.
“Grange Primary School remains closed today.
A statement on its website reads: ‘Urgent - school is closed today due to a serious incident.’
Have police made any arrests?
Yes. The Met arrested a 20 year-old man on suspicion of murder but this man has been released without charge.
Detectives made a second arrest when they took a 29 year-old man into custody.
It has been reported that the man “was known” to Ms. Jedrkowiak.