A Scotland Yard spokesman said that the man, believed to be in his 30s or 40s, has been sitting atop the statue for the better part of two hours.
He said Friday: "We're still talking to him. We're still trying to get him down without causing any injury to him."
Photos posted to Twitter appear to show the man straddling a statue of the 19th century duke of Cambridge, down the street from the prime minister's official residence.
The man's motives aren't clear, and, with London's late autumn temperature reaching a brisk 10 degrees Celsius (50 degrees Fahrenheit), it's not clear how long he can stay there.