Emergency services were called to the Fernways unit on Cecil Road, Ilford, at about 22:20 BST on Saturday to reports of an assault.
Two people found with stab wounds were pronounced dead at the scene.
A 50-year-old man was arrested on suspicion of murder and is in custody at an east London police station.
Police believe the victims and the man arrested knew each other, but said they were not related and were not staff at the unit, which is part of the care provision of Redbridge Borough Council.
Officers say they know the identities of the deceased and their next of kin have been informed.
Post-mortem examinations on the pair will be held later, the Met said.

A car bomb exploded as his convoy was passing, killing at least one body guard. The so-called Islamic State (IS) group says it carried out the attack.
The city's last governor, Jaafar Mohammed Saad, was killed in a similar attack in early December.
IS intensified operations in Yemen when civil war broke out in March 2015.
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Witnesses to the attack described hearing "a loud explosion". One local man, Attef Hassan, told Reuters: "I thought it was an explosive device. I turned round and saw the governor and his companions getting out of the governor's car, and, thank God, they were not injured."
Yemen has been rocked by fighting, mainly between forces loyal to UN-recognised President Abdrabbuh Mansour Hadi - who fled into exile in Saudi Arabia - and those allied to Zaidi Shia rebels known as Houthis. IS opposes both groups.
A Saudi-led coalition made up of nine nations began airstrikes in March, hoping to defeat the Houthi rebels.
On Tuesday, warplanes carried out fresh strikes on the capital, Sanaa, which is under Houthi rebel control. Residents say a care centre for blind people and a chamber of commerce building were hit.
The UN says almost 2,800 civilians have been killed since fighting began.
"The ongoing armed conflict in Yemen continues to take a terrible toll on civilians, with at least 81 civilians reportedly killed and 109 injured in December," UN spokesperson Rupert Colville said in a statement on Tuesday.
"This raises the number of civilian casualties recorded between 26 March and 31 December to 8,119 people, including 2,795 killed and 5,324 wounded."
A woman in her 50s and a man in his 80s have been stabbed to death at a sheltered housing unit in north-east London.
[NEXT_CONCEPT]
The governor of Yemen's port city of Aden, Aidarus al-Zubaidi, has survived an assassination attempt, security sources say.