Mrs Morrison was stabbed repeatedly in the abdomen following a pre-arranged meeting in the Thurleigh Road hostel in Balham. She had been Mr Joseph's keyworker for two years and had been a social worker for more than 20.
A post mortem gave the cause of her death as multiple stab wounds and police said two kitchen knives were recovered at the scene. The council has set up an immediate inquiry. It will be followed by an independent public inquiry.
The hostel, which is permanently staffed, has room for up to 13 residents who live there on a voluntary basis. They are considered not dangerous enough to warrant secure care.
Mrs Morrison's daughter Tanya said yesterday: " She lived for her job and she died for her job and for all the people that she worked with."
"We are still so very numb." said Mrs Morrison's sister Sandra Foster. "She worked her whole life - morning, noon and night - at this job."
Her son Stephen described his aunt as a "second mother". "It is not real yet. She was a lovely, kind, passionate human being who does not deserve to be dead." he said.
Melba Wilson, policy director of the mental health charity Mind, expressed her "deepest sympathy" to Mrs Morrison's family, but added: "It is important to state that the vast majority of people with mental health problems can and do live safely in community settings."
But the chief executive of SANE, Marjorie Wallace, said: "This terrible incident yet again exposes a policy which is unsafe and is failing to protect patients, families, the public and those who work with seriously disturbed people."