The Model 870 Shotgun is a pump-action shotgun in ZombiU. It is notable for being the shotgun with the longest range in the game, though it is also the weakest shotgun per-shot. It also boasts the best accuracy and the tightest spread.
It is originally found in Spitalfields Green, near Vikram's gas station. He intended it as a bonus reward for the player, alongside the Gasoline, when he succumbed to his infection. You can access the storage area where the weapon is after returning to Vikram following the mission at Baconfield.
The Remington Model 870 is a paramilitary shotgun produced since the early 1950's, L74A1 is the British designation of the same weapon. The L74A1 is used by the United Kingdom Special Forces and Specialist Firearms Officer (Police) as a breaching weapon.
The M870 is the weakest shotgun per-shot (though not by much), having less damage per-shell than any other shotgun. At a glance, it looks like something of a wash, especially when the Benelli M4 Tactical Shotgun becomes available at about the same time.
Where the M870 makes up for these shortcomings, however, is its range - it's the longest-ranged shotgun in the game, and it boasts the tightest firing cone as well. At ranges when other shotguns are doing half their damage (or less), the M870 is still doing full damage.
This means it's the easiest shotgun to do maximum damage with, and is extremely good at taking out high-toughness zombies, even at a range not really suited for shotguns. The downside is that it's somewhat weaker in close-combat than other shotguns, but that's a modest price to pay for its sheer efficiency.