His death is not being treated as suspicious and detectives are investigating whether a police gun was used.
Officers were called shortly after 4pm on Wednesday and forced entry to an address in King's Terrace.
The man had a gunshot injury and was pronounced dead at 4.45pm.
His next of kin have been informed, the police said.
He was not under investigation as part of either the "plebgate" probe or the inquiries into alleged phone hacking and corrupt payments to public officials.