A police spokeswoman said: "It is alleged a man assaulted another man (Victim 1) in 2008 in Lambeth".
Kevin Spacey was artistic director between 2004 and 2015 at the Old Vic, which is based in Lambeth.
A statement from the Metropolitan Police revealed that the alleged sexual assault took place in Lambeth, the area where the theatre is located.
The allegations against Spacey started with Star Trek actor Anthony Rapp.
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.
Scotland Yard also said that the allegation was made on November 17, one day after the Old Vic - where Spacey served from 2004-2013 - revealed that it had received 20 complaints of inappropriate behavior by its former artistic director.
Eight people have claimed that Spacey sexually harassed House of Cards employees during his time on the set, including one who he allegedly sexually assaulted.
In the past few weeks Spacey has been fired from the Netflix TV series "House of Cards", was dropped by his talent agency and publicist and is being cut out of Ridley Scott's finished film "All the Money in the World".
Kate Varah, the Old Vic's executive director, issued an apology on November 16 to the alleged victims.
There were many other allegations made after Rapp's story became public.
The BBC has contacted Spacey's legal representatives for comment.
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