Yes I got my US passport renewed via London Embassy recently.
I sent it via courier service on February 1st. I planned to travel 3 weeks later and stated it on the application.
After about 2 weeks I got a call from the embassy. They said, "Oh, we've noticed you are going to travel soon but we've just opened your application." So basically the application just sat there for 2 weeks. Then after talking to me they expedited the processing but still I only received the passport after 4 weeks. I checked status of the application (
https://passportstatus.state.gov/opss/OPSS_Status_ip.asp) in the meanwhile so I know it was sitting in the mailroom at the embassy for another week or so. I also applied for a passport card and still have not received 7 weeks later (!!!), embassy folks say it's coming...
BTW expedited passport processing stateside currently takes 1 week.
I think the embassy switched to British service standards

here's a tip: you probably paid with a credit card, see if it has been charged. Then see what the above passport status link says.
You can also contact them at the embassy at londonpassports@state.gov. Phoning them did not work out for me.
Best of luck!