A post-mortem examination will take place on the body at Finchley Mortuary this afternoon.
Detective Chief Superintendent Adrian Usher, Borough Commander for Barnet said:
"The discovery of the body of a young woman on Sunday 21 July hidden in a suitcase is a tragic and shocking thing to happen, I am sure local people will be feeling unsettled by this news.
"Crimes of this serious nature are incredibly rare in our Borough, which may only add to local concern over what has happened. I would like to reassure the local community that we are working closely with specialist homicide teams to establish the full circumstances surrounding this murder...
"...As a means of reassurance to the public within the vicinity of Thornfield Avenue officers from the Finchley Church End Safer Neighbourhoods team have increased foot and vehicle patrols and will be engaging with residents to answer any concerns and provide up to date information."
Detective Chief Inspector Nicola Wall, from the Homicide and Serious Crime Command said:
"The Homicide and Serious Crime Command are still in the early stages of this investigation and urgently require the assistance of the public to help us establish the circumstances around the murder of this young woman.
"We are specifically appealing to anyone who witnessed anything suspicious towards the latter part of last week. Did you see anyone moving a heavy black trolley type suitcase on or after the 18 July, especially around the Thornfield Avenue/Dollis Road entrance of the wooden area?
"We are also interested in hearing from anyone who is concerned about any young adult females who have gone missing from the immediate area recently.
"If you have any information that can assist us with our inquiry please do get in contact with the police".
Any witnesses or anyone with any information should contact the incident room on 0208 785 8334; if you wish to remain anonymous call Crimestoppers on 0800 555 111.