I'm posting this in the hopes it gives someone a little reassurance about the interview process.
I arrived at the London embassy at 8am for my 8:30am appointment, I'd recommend if you have an early interview and need to travel far to go over the day before and book a hotel so you can be there with plenty of time in the morning. There was a looong line of people outside despite it being so early, however since I had read that K1 applicants should be queuing on the left (it was hard to tell where was "left" from outside), I walked up to the lady checking everyone's interview letters and showed her that mine was K1. She marked my paper and sent me straight to the front of the line where there was a man checking people for laptops and asking each person to pull out their phone and open an app on it before they went inside. Once inside there was a little security area and metal detector, then a few doors and signs later there was a desk with another lady taking interview letters and giving people stickers with their interview number. She told me to go up to floor 1 and go left and left again and take a seat to wait for my number to be called.
The area where I sat was much less busy than where you walk past to get to it, and it didn't take long to be called up to submit each document one by one and answer a few brief questions like "have you been married before", "have you served in the military", etc. I'd brought two i134 forms each with their own evidence, though I don't think that ended up being necessary since they took both but only one piece of evidence for each (I took tax returns, employer letters and w2). They also didn't need the copies of the birth certificates for the two sponsors. They took my fingerprints and asked if I had the medical exam, and I told them yes on the Monday of that week, and they wrote a little note at the bottom of their form saying "medical pending" as they hadn't received it yet.
List of documents that they took from me:
Passport
One US sized passport photo (which was cut, scanned and returned)
Birth certificate
Deed poll (name change)
Police certificate
DS160 confirmation
i134 + one evidence
I was then sent back to sit and wait to be called again. After a while of waiting (there was only one booth open for this second part and there was a whole family called up before me), the lady called me and asked me to put my hand on the scanner to check my fingerprints, this time only one hand as opposed to doing both at the previous booth. She then told me to raise my right hand and had me agree to an oath to tell the truth. She asked a couple basic questions about my fiance, like to confirm his name and the city he lives, and asked how we met and how he proposed. She also asked how many times we met and for how long, and then typed for a bit on her computer before saying that she was happy and had no doubts about our relationship. She said that if everything was good I should receive my visa within two weeks and that was it! I was handed a green form with "additional evidence required" and "medical examination" checked off, and they returned the originals of all of my documents but kept my passport.
After the interview I checked the CEAC tracker almost everyday, and for the first few days it was marked "refused". On the 28th (interview was the 23rd right before the weekend) the case changed to "application received" then later that day "approved". From there it took two days before it was changed to "issued" (30th) and today I received my tracking number from the courier with information that I should receive my package with my passport on monday. So all in all it took a week from interview to issuance and visa printed and in passport, despite the embassy not having received my medical until at least the day after! Though the weekend will delay me actually having passport in hand, the big portion of the stress is over. I hope this helped anyone who either didn't have their medical at the time of interview or is just trying to prepare their best to have a smooth interview. Good luck everyone!