I wanted to write up my experience, so that others can benefit (and so I can remember what I need to do if/when #2 comes along).
I'm a US-born, US citizen, who has lived in the UK for 9 years. I have British Citizenship. My husband is British. Our son was born in February, in the UK.
Making the appointment to register his birth, first passport, social security number wasn't hard. The latest appointment they have is 10am. Because we live so far away (near Peterborough, 80 miles north), I booked 9:30am appointment. In the end, it took over 3 hours to drive in (left at 6:30, didn't arrive in Grosvenor Sq until 9:35). I had planned to park at the nearest NCP parking lot, which is at the Millennium Hotel, just a few hundred metres away from the Embassy. On the way to that car park, I noticed a few open street spots and pulled into one right on Grosvenor Sq. It was pay and display, and I got the max of 4 hours for £17.
I walked very quickly to the Embassy, and was disheartened when I saw a long que. Luckily, that que was for non-US citizens. There's a separate entrance on the left for 'American Consular Services'. You check in with a woman with a clipboard, and then go through to a security 'house'. All was fine in there except, my car keys. Since it's a key fob, I had to check it. They took the keys and gave me a ticket. Although they advise that you leave your electronics (kindles, phones, etc) at home/in car, they do appear to have the facilities to check these things.
Walked through to the reception desk (1st flight of stairs), and checked in, 15 mins late. They seemed quite non-chalant about time. They have me a card with a number, and a form if I wanted courier services. The toilets & baby changing facilities are down a flight of stairs, or there's another flight of stairs to the next room. At this point, I'm glad I brought 'Little Man' in a sling instead of the pushchair.
I went to the toilet, and then up to the waiting room. As soon as I got in, I was called to a window, where they very efficiently took all my paperwork. She also checked in and advised a few things that I needed to correct. They were really nice and polite, especially seeing as I had a very hungry 10 week old screaming in our ears. She took:
Consular Notification Form
My current & past US passports
High School Transcript
College/University Transcript
List of all absences from the US (I could only go as far back as 1997...)
Marriage Certificate
Picture of Son (to US Specs)
Son's UK Passport
Son's UK Birth Certificate
Passport Application Form
Notarised Form from Husband allowing me to get him a passport
My Husband's UK passport
Social Security Application Form
Things they DIDN'T Want:
My UK Naturalisation Certificate
My SS Card
My Birth Certificate
I was given a form to show the cashier. I then went to cashier's office and parted with the first $100. I was advised to keep that receipt, as I'd need to show it later.
I then filled in the courier paperwork, and went back down to reception to drop in. I forget exactly how much that was, perhaps £17 or so.... They gave me an envelope/bag addressed to my Son.
I then went back up into the waiting room... to wait... The room itself is fine. Quite large, with a drinks & food vending machine along the back. There's also a small children's play area. There are no clocks, although you can see one in the offices behind the 'teller windows'.
At 11:30, (1 hr, 40 min after arriving) I was called back to one of the tellers and was asked a variety of 'ID' questions such as:
Where was I born?
Where did I grow up?
Where is that city in relation to other cities?
Where did I go to High School?
When did I graduate from High School?
How many years was I enrolled in College?
Did I go abroad at all during College?
Where and when was I married?
Satisfied that I could bestow US citizenship to my Son, she had me sign two forms (Passport & SS Forms), and also filled out another piece of paper to take to Cashier (to pay for passport). I went and paid, and brought her back the receipt. I also gave her the courier envelope I had obtained from Reception. She gave me all my paperwork, passports, etc back. I was advised that I would receive the 'Notification of Birth Abroad' and Passport in 3-4 weeks. The Social Security Card would be a bit longer, and would come via standard post.
All in... it was a lot less stressful than I thought. Next time, I would leave 3.5-4 hours to drive down there.