I have at least the Fallout 4 version before the Next Gen update lying around (Fallout 4 1.10.163.0), because you need it to play Fallout: London. The upcoming Next Gen update version of Fallout: London currently has too many problems, but the Fallout: London team is working on a solution. If you don't have the older version of Fallout 4, this is not a problem as Fallout: London comes with a downgrade patcher.
About the total conversion (quoting from Fallout: London's website):
Trailer:Fallout: London is an ambitious, trail-blazing DLC-sized mod for Fallout 4, Bethesda Game Studios’ 2015 post-apocalyptic RPG. Fallout: London stands apart from its contemporaries and offers an entirely new experience: setting a Fallout game outside of the United States. True to its moniker, Fallout: London takes place IN London. From stuffy parliamentary aristocrats to a resurrection of the Knights of the Round Table to an uncompromising cult of revolutionaries (and more!), Fallout: London embodies the history and aesthetics of London and puts an unmistakably nuclear spin on the beloved city.
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Download and installation instructions
As a side note, I've added the Fallout London tag, which you can use in the forum to tag threads about Fallout: London to better distinguish Fallout: London content from the original Fallout 4.