Hi! We (my 20 year old son and myself) were also in at 10.30am and they make sure that you are seen so there's enough time for you to get down to the Embassy. I would get an Uber as it takes the stress out of the situation. It's about £18. They tell you at the medical it's between 12pm-1pm to get to the Embassy but it's actually until 2pm. I asked her and said I was concerned we weren't going to make it but she smiled and said not to worry! They let the embassy know that you are heading down there so when you get there you already on a list. I would get there earlier (for medical) if you are at all anxious as it seems to be first come first serve basis...
At the Embassy go to the window on the road first, they will give you a pink slip and then you go to another door which will take you through security, then another entrance with more checking. Then you go upstairs to get officially checked. We saw 2 different officers. It's all very well organised!
You will see 3 separate doctors. 1. Chest X ray. 2. Vaccinations. 3. Doc for medical check up/ go through report/ eye test/ weighed/ measured and blood test if you need it. Good Luck!