Ubisoft's survival horror FPS ZombiU was contained as a Wii U exclusive for a surprising three years, but today it escaped Nintendo's console to gnaw on skulls round our way too. Now named Zombi [official site], it's set in London during a zombie apocalypse. I haven't seen ZombiU in a while, but I remember it as least being a better representation of London than most games manage - they really captured the shambling zombies sicking up guts round Brick Lane.
So there you are, just some regular Jane or Joe in the zombie apocalypse - you (re)spawn as a random character each time - trying to salvage supplies, get safe, and beat the heck out of zombies when you end up caught in a plot to save the day following an old prophecy by John Dee. They can never leave well enough alone, that Ubisoft - always have to wedge in a secret society and ancient science.
Like many survival horror-y games, you're generally low enough on ammo that you'll be trying to bludgeon zombies (this version adds a shovel and naily baseball bat to go with the cricket bat). You're also vulnerable when in your inventory and otherwise interacting with stuff, as the game keeps running. Should you kick the bucket, your character will turn into a zombie that your next survivor can track down and squish to recover their gear. It's a mild permadeath, but adds a nice little extra threat.
This new PC version, however, does not have the local multiplayer bits of the original ZombiU - it's all solo. This blog post details other changes too. It does have a smaller price tag, though.