The incidents reported to the Lambeth theatre cover a period of 1995 to 2013 and have not been verified, The Old Vic said.
Star Trek: Discovery actor Anthony Rapp was the first to come forward with allegations against Spacey, saying the older actor tried to "seduce" him when he was 14.
The news comes after the Old Vic theatre, where Spacey served as artistic director between 2004 and 2015, published the results of an internal inquiry into claims that Spacey had harassed and assaulted staff members there.
"On Wednesday, November 1, City of London Police referred an allegation of sexual assault to the Metropolitan Police Service", they said.
A two-time Academy Award victor, Spacey was artistic director of London's Old Vic Theatre between 2004 and 2015.
United Kingdom police are investigating new accusations of sexual harassment made against Kevin Spacey.
"It is alleged a man assaulted another man, victim one, in 2008 in Lambeth".
This new claim is in addition to a 2008 assault being investigated by the Met. "The allegations are of sexual assaults against a man (Victim 2) in 2005 in Lambeth".
The force didn't identify Spacey as the alleged perpetrator. The Old Vic said a "cult of personality" around Spacey had discouraged people from speaking out.
Another man, who did not reveal his name, told the BBC he was left traumatised after waking to find Spacey lying on him, in his underwear, with his arms wrapped around him.