We used Snappy Snaps for our 3 week old's US passport pics just last week. It was definitely expensive £14 for 2 pics, but it was fast and convenient. Dunno if there's a surcharge for a tiny baby vs an adult vs a non-baby child.
I know they have a US passport photo booth in the visa section of the US Embassy in London, so they may have one in the US citizen section for passport applicants when you go for her appointment, but I don't know for sure, so it's probably best to get one done somewhere else in advance.
Yep, there is definitely a US passport photo booth in the US citizen section of the embassy -- it's right when you walk in the door after being cleared by security. Can't miss it. I don't know the price (and know that it requires pound coins because people were asking for change), but as of Thursday, April 21, it was there!