The Prime Minister says he wants investigations to "get the full truth out" about "horrific" allegations, that police tried to smear the family of Stephen Lawrence.
An undercover police officer claims he was ordered to find information to discredit the family, Duwayne Brooks and campaigners.
He said it happened in 1993, just months after Stephen was murdered at a bus-stop in Eltham in an unprovoked racist attack.
Both the Home Secretary Theresa May and Mayor Boris Johnson spoke about possible criminal prosecutions of Met officers, if the claims prove to be true.
We have this report from our Senior Correspondent Ronke Phillips.
More top news
Charlie's parents asked European court judges in Strasbourg to consider their claims but they refused to intervene.
Rachid Redouane, 30, gave the Immigration Service the false alias Rachid Elkhdar, a court heard, and said he was five years younger.
Judges in the European Court of Human Rights have rejected a plea from the parents of terminally-ill baby Charlie Gard to intervene.