At least 80 people were killed in the June 14 disaster but police say only 21 of those have been formally identified.
Commander Stuart Cundy told reporters on Wednesday that police had “forensically recovered the last of the visible human remains.”
“Work in Grenfell Tower continues, seven days a week,” Cundy said. “I do not want there to by any hidden victims of this tragedy.”
Cundy said that although police had made 87 recoveries, the “catastrophic damage” inside the building means they do not equate to 87 people.
Police have spoken to at least one person each from 106 of the 129 apartments in the tower. Based on those conversations, they believe there are 18 people who must be presumed dead.
That leaves 23 apartments with no-one accounted for. “We assume that sadly no one from any of those flats survived,” he said.
Cundy added that specialist officers have started a search by hand that will involve going through 15.5 tons of debris on each floor to find remains still in the tower.
The announcement comes on the day the British government appointed a task force to take over parts of the Kensington and Chelsea local council in response to its admitted failings in the wake of the tragedy.
There has been widespread criticism of the council’s lack of ability to deal with the situation, with leading figures resigning from their posts.
“The scale of the recovery effort needed on the Lancaster West estate in the months to come cannot be underestimated,” Communities Secretary Sajid Javid said Wednesday.
“I want to help the council meet that challenge,” he added.
“As well as providing that immediate support, we must have an eye to the future. This intervention is putting in place the foundations that will support the longer term recovery,” he said.