Not helpful, but anyone else think that place looks like a heinous fortress in the otherwise lovely Grosvenor Square? lol Whenever H says he needs to go there I always start humming the Darth Vader theme tune. Last I heard they were supposed to be moving south of the river into somewhere nicer.
Book an appointment online. When you get there, if there is a long queue, don't wait in it -- go to the very front (towards the left-hand side) and you'll see a shorter queue (or no queue!) for Americans seeking consular services. They'll have your appointment info and you can go right in :-)