Mr Hallisey was assaulted at the supported unit in Lansbury Drive on Monday evening.
Despite the efforts of paramedics he died at the scene.
His next of kin continue to be supported by detectives from the Met's Specialist Crime Command, Scotland Yard said in a statement.
A post-mortem carried out on Wednesday found his cause of death was compression to the neck.
The Metropolitan Police said both Mr Hallisey and Pall were residents at the facility.