First reach the royal Doctor. Problem I had is he talks a bunch, so a little waiting is involved.
There is a container right near the doc, you must use it at this point or a bit later to give him some documents. Just letting you know because it is a bit unoticeable.
Eventually the map marker, will lead to an elevator. The elevator leads to Buckingham palace.
You do NOT have to scan the CCTV box here, although I recommend doing so. It's not really a vital one so if your having trouble finding it move on.
You will be introduced to spitting zombies here, see enemy section. They are quite dangerous so take them down.
The main problem I had here was keeping up with the map marker. You should come to a long hallway room, with some furniture in the way. It is up the staris for sure and to the left wing.
Know your there by some Riot Officers and a spitter possibly. Make your way down that hallway, and there will be an entrance to a room that is on fire.
Look for a ladder in this room, and you can walk across the catwalk or planks. Walk across until one of the catwalk pieces collapse. Now you can fall down and make it to the other side safely.
Inside you should now be able to make it to the marker easier. Follow the marker to pick up the appropriate quest item.
A panel will open up after collecting the notes. Go inside the linear path and you will run into a NEW weapon. The Hunting Crossbow, which rocks. See video section AND weapons info here.
Once you get the crossbow, backtrack to the left side and find the backpack upgrade in the corner of the room. Finally push the red button to gain access back to the main hallway. Follow marker to the Doc.
This is the point where you use the bin I spoke of earlier. So hand the Doc the book through the bin.
Follow some easy marker based stuff until you get the Virucide shot, see gear section for details.
Speak to the Doc again and he will give you the next mission.