The new investigation centers on an alleged incident, or possibly incidents, in Lambeth dating back to 2005.
A two-time Academy Award victor, Spacey was artistic director of London's Old Vic Theatre between 2004 and 2015.
"It is alleged a man assaulted another man (Victim 1) in 2008 in Lambeth", the force said in a statement.More news: Rainbow Six Siege Year 3 Detailed, New Co-Op Mode Incoming
It's unclear if Scotland Yard's investigation relates to one of these complaints.
"On Friday, November 17, a further allegation was made about the same man".
"The Old Vic apologizes wholeheartedly to the people who told us that they have been affected", said Varah.
"The allegations are of sexual assaults against a man, victim two, in 2005 in Lambeth".More news: Uber strikes deal with Volvo
The Old Vic said it received the claims of inappropriate behaviour in recent weeks, although the alleged incidents were said to have taken place from 1995 to 2013.
The second allegation was made on Friday, police said.
The scandal has cost the embattled actor his role as controversial politician Frank Underwood on Netflix show House of Cards, and he has been edited out of Ridley Scott's new movie All the Money in the World.
Alleged victim, Daniel Beal said that Spacey showed him his penis in public when he was 19, before giving him his £5,000 watch to buy his silence.More news: Trump blasts Hillary Clinton for questioning legitimacy of election result
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