Spacey was artistic director of The Old Vic from 2004 to 2015.
The alleged incident took place in 2005, when Spacey was still serving as artistic director of London's Old Vic theater.
Scotland Yard is also looking into allegations that Spacey sexually assaulted another man in 2008.
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"The Old Vic apologizes wholeheartedly to the people who told us that they have been affected", said Varah.
The former House of Cards star's reputation took a hammering last month (Oct17) after actor Anthony Rapp accused the Oscar victor of making inappropriate advances towards him when he was just 14, in 1986. "The allegations are of sexual assaults against a man (Victim 2) in 2005 in Lambeth".
The second allegation was made on Friday, police said.
Netflix and Sony Pictures have cut ties with the star, firing him from House Of Cards and replacing him in upcoming film All the Money in the World.
A man on the east coast of the USA said that Spacey repeatedly had sex with him when he was 14, adding: "He tried to rape me".
The man, who was a teenager at the time, said Spacey's behaviour during that weekend was "either very stupid or predatory - or maybe a little of both".