My experience for K-1 interview at the U.S Embassy in London:
I was really nervous but didn't need to be so hopefully this helps anyone who is nervous like me!
I got to the embassy early and waited outside as they don't let you in until 15 minutes before your interview time. I then went to the line and was asked for my ds-160 and passport. Then I was directed through airport style security. I had a bottle of water on me which they made me drink (assuming this was to check that it was just water).
Then you walk up to the main reception area where there was a line. As I got into the building my name was called out and I went to the front of the line and was told to go upstairs to the first floor and take two lefts. I think the k1 visa gets priority over other people who were waiting in line. Once upstairs I sat down and waited for my number to be called on the screen. There were a few people there with me and I got chatting to some other people there, one girl who had just had her interview was really sweet and told me I had nothing to worry about which was nice.