Matt Bird writes all sorts of nonsense, but he dedicates a large chunk of his time to writing game walkthroughs.
When you emerge from the elevator into Buckingham Palace Interior you'll be in a short hallway. Start by checking the room to your left. Inside you'll find Queen's Letters in a briefcase on the ground. In the back of the room, you'll find a ladder leading up to the second floor. Be prepared for a substantial scare if you go this way, as a zombie will grab you and pull you into its room. Once you get away, beat it to death. You're now on the second floor.
Go down this short hallway and you'll see a ballroom of sorts before you, with stairs sweeping downward. Two zombies will shamble in your direction; one is normal, one definitely isn't. Move back into the hall and take on the normal zombie, then target the one that appears to be steaming. This is a spitting zombie, and it will hurl acid at you if you don't close the range. Shoot it once to stagger it, then move in for a normal kill. Another normal and spitting combo will appear after this; take care of them in the same fashion.
If you can't be bothered, you can ignore the bottom floor of the ballroom, though you'll miss out on some items. Go down the stairs and sweep around the zombie 'playing' the piano, ignoring it in favour of the zombie on the couch and the zombie on the floor. Both will rise up at you—and you can take them both out without a fuss if you're fast. Then go for the piano zombie. Once they're all gone, check near the couch for Fixed Turret Ammo, the zombie on the ground for Handgun Ammo, and under the piano for Cake.
(Note that you can approach the ballroom from the ground floor, as well, though dealing with the zombies inside is much harder than if you get the drop on them from the top floor.)
Once the ballroom is clear, check the right side for a new hallway. A SWAT zombie will immediately come out the doors at you. Lure it into the ballroom to take it out, then steal its Large Medipack. Inside the hall, you'll see a lone zombie on the other side of fallen furniture. It looks weak enough prey, but as soon as you cross over the barrier to attack it, three zombies will emerge from a burnt hallway behind you. Get rid of the first zombie, then turn around and wait for the nearest SWAT zombie to approach and knock its helmet off. Then either shoot or use a Flare to distract them while you set them aflame with a Molotov. The noise will likely draw two more zombies from nearby rooms, as well; use the ballroom to separate them. Watch out, one is a spitter. Loot the corpses afterward for assorted ammo and a few Mines.
Down the corridor, you'll find a room with a ghostly fire in the distance. There are Documents on one of the tables, and along the left wall you'll find a crawl space you can't yet get through. Continue on to the room with the fire and you'll see a door requiring a code. Be wary, the moment you pass or check this door, a group of zombies will come at you from the previous hallway. Turn around and deal with them as you see fit; one is a SWAT zombie.
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Before addressing the code door, turn back to the fire room. You'll see one SWAT zombie ambling about. Kill it and you'll hear another zombie screaming somewhere nearby. Look up on the scaffolding and you'll see the thing near the top. If you trust your aim, you can shoot it down; otherwise you'll have to deal with it later.
(At this point you can check the security room, using the code scrawled on the wall beside it. Unfortunately, there's nothing to be found in here. Bah.)
Climb up on the scaffold in the fire room and check the right side of the room for Cake and Crossbow Bolts. (Don't worry, you'll find the weapon soon.) Make your way to the other side of the room and peek in; you'll see a zombie and a SWAT zombie just inside. One at a time luring is preferable - just make sure you don't go too far into the room, as the next room over is crawling with zombies that can be killed much more easily.
You'll find some Documents at the top of the stairs. Head back down, then check the conspicuous-looking hole beside the fire to find a crawl space. Follow it to find a container with Handgun Ammo and Cake, a path to find Carbine Ammo, and a perch overlooking the adjoining hallway, which is filled with zombies. This is the perfect place to use a Molotov, if you have one. If not, this is also a good spot to snipe them. They won't know how to get up.
Once the zombies are out of the way, check the SWAT zombie for Handgun Ammo, and the hallway for Queen's Letters and Documents. Beyond this you'll find two doors that lead into the same room; inside are Queen's Letters and The Dark Prophecy on the desk, and De Remidi Secreti (the book Dr. Knight wants) in a niche along the back wall. Grab the book and a door will open along the side cabinets; crawl in.
Follow the path to the right a short ways. A zombie will groan; that's your sign to back up and take it out in the narrow hallway. Much more dramatic than it needs to be. Past it you'll find a Backpack XL, allowing you to carry more items in your backpack. Pretty nifty. You'll also find a button opening the way to a room you passed before. Ignore this path and backtrack, then go left from where you came in. You'll find a ladder, and beyond it a Hunting Crossbow. Excellent for quiet kills, and you can pick your ammo up after you shoot. You'll also find more Documents.
Step into a revolving white tube at the end of this hall and you'll be back in the ballroom! Excellent. You can now travel unmolested back to the elevator and escape Buckingham Palace Interior.
You won't run into it too often in ZombiU, but fire is excellent for killing zombies. Lure a zombie through fire and much of its strength will be sapped instantly. Run a ways and the zombie will probably fall over dead. This is an excellent method of conserving ammo and keeping quiet, and you can do it a few times in Buckingham Palace Interior. Be warned, however, this tactic won't work on SWAT zombies.
© 2013 Matt Bird