The Grosvenor Square Goodbye by Francis Clifford

A lone, crazed sniper starts shooting at random from the Shelley Hotel, dead opposite the US Embassy. The first victim dies at the foot of the Roosevelt monument. The rifleman then breaks into a bedroom and takes the couple there as hostages. Because of the US Embassy, police response is quick and massive and the book becomes a battle of wits with the sniper (who demands to see the American ambassador) as police and security services try to discover who he is and what he wants