Matt Bird writes all sorts of nonsense, but he dedicates a large chunk of his time to writing game walkthroughs.
After your visit to the Tower of London, you'll come back to a more sympathetic Prepper. No surprise, either, as he needs you to do something else for him: get some backup fuel for the generator in the Safe House. The lights are out, and unless you want to spend the rest of your time in the dark you'd best help get them back on. Fortunately, Prepper has an acquaintance who may be able to supply the gas.
Head back to Brick Lane Markets. Along with any other zombies that may have wandered into the area, you'll find a red zombie lingering on the street. Isolate it and kill it for a Firepower Upgrade. Further along the street, not far from the ambulance and behind a barrier, is a screaming zombie. You haven't seen one of these for a while, but the effect is the same - it will call other zombies. Try to kill it before it can get a scream off.
Once the way is clear, follow the mission reticule to an alley across from the screamer. Check the yards on the left for a secret code on a wall, then inside the shed beside the shed for the second half of the code. Use that code on the door at the end of the alley. Inside you'll find a sewer, and in the sewer an Exit door. Go through.
Welcome to Spitalfields Green. Follow the path through the subway and sewers to find a ladder. Check the water for an Energy Drink (ew) and the side of the water for a Molotov. Head up the ladder to reach a small park.
Unfortunately, your radar is jammed when you come up. Trash the nearest body to you before it can come to life, then check the park. There are two zombies in here; lure the nearest one to the archway, kill it, destroy the radar dish at the edge of the park that's blocking your radar, then lure the zombie still in the park to the concrete. If you're lucky, it will hit one of the mines somebody's laid down in the grass and die. If not, fight it outside the park. Do NOT engage it inside the park or you'll risk getting blown up.
Ignore the park for the moment and check the houses. The first house on the left contains an exploding zombie; stand back and kill it at a distance before it can get close. You can go through the shed to check other houses, but there's nothing of value - save another radar dish at the end of the block. You can't hit it with your Cricket Bat, but you can shoot it. There's also a door here that requires a Key Card you don't yet have, as well as an obscure map drawn on the wall behind the shed. You'll understand what it means shortly. Check the wall behind the Key Card Door for a CCTV junction box you can scan.
Tiptoe back into the park, sticking to the end to avoid the mines, and unlock the door beside the stairs. Go up it and you'll be overlooking the area you'd have walked into by using the stairs. Down there are two zombies. Take out the normal zombie from above, then go down into the alleyway and kill the SWAT zombie with your Cricket Bat.
Carry on down the alleyway. You'll soon hear some screaming. Be ready, because as you head closer to the steam coming out of the left building a zombie will fly through a window and land in front of you, and a SWAT zombie will lumber up. Immediately backtrack to lure the normal zombie; you should avoid alerting the SWAT zombie this way. Then kill the SWAT and keep going.
There's a locked gate at the end of the alley, forcing you onto the street. Be very careful coming out here, as there are seven or eight zombies near the police car, many of them hidden from you. Pick a clear spot and toss a Flare out, then follow up with a Molotov to kill most of them. There should be only a SWAT zombie left when you're done. Go a little further up the street towards your destination and you'll also find a spitter.
Check the alleyways once you're done and you'll see a zombie behind a door. Wait for it to bust through, kill it, then climb the ladder to the roof. Up here you'll find a door to a resting area where you can save, as well as a path to a security-locked door. Scan the door and it will show you a map leading back to the park. Knowing what you already do, check where the park in the park indicates: the building with the rest spot. Cross to the lower roof and scan the wall for the code, then use it to enter the door. Inside you'll find a Firepower Upgrade, a Large Medipack, Shotgun Ammo and Carbine Ammo. Not a bad haul. While you're up here, scan the opposite side of the street—you'll see a CCTV junction box high on one of the buildings.
Return to the street and carry on down towards your objective. Kill the zombie at the side of the gas station, then pick the lock on the door and head inside. Go through the white door to enter the gas station.
By this point in your trip, especially if you've been conserving ammo and killing with your Cricket Bat, you probably have a consistently-packed backpack. This will be especially true if you're playing online and Survivor Zombies keep appearing. To economize on space, immediately eat or leave any food items behind, only take Medium Medipacks if you absolutely need them, and minimize your armament to two, possibly three guns at maximum. You don't need every item to survive ZombiU.