Thirteen interviews have been carried out under caution by detectives investigating the Grenfell Tower fire, police say.
The Metropolitan Police said they would not be disclosing how many individuals the 13 interviews concern.
The force added that just over 7,100 statements have been taken from witnesses, community and family members, emergency services personnel and others as part of the probe.
The news comes a week before the two-year anniversary of the fire on 14 June 2017, which claimed 72 lives.
Karim Mussilhy, whose uncle died in the fire, said it showed "some positive steps" were being taken.
Mr Mussilhy, who is vice chairman of the campaigning group Grenfell United, said: "It would be interesting to find out who these bodies or organisations or individuals are, but at least it means progress is being made in the criminal investigation.
"We were told that the police investigation would almost run alongside the public inquiry, and obviously we know about all the delays the public inquiry has had, so this is something positive to a certain extent."
In March, police said no charges were likely to be brought for at least the next two years.
The Met said it would be "wrong" not to wait for the final report of the Grenfell Tower inquiry, which will come after the probe's second phase.
This is not due to start until early next year.
Survivors and bereaved families called the wait "extremely frustrating and disheartening".
They were informed of a further delay last month when the inquiry team told them its first report, expected in the spring, would not be ready until October.
This delay is not due to affect the start of the second phase, the team said.