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."