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IIRC there have never been private servers for Hellgate: London, and with the official servers down and no way to sniff out what sort of data is sent to/from them there's no way to create one. The closest there's ever been was when T3Fun hosted Hanbitsoft's English port of their Korean port of the original game, complete with F2P microtransaction shenanigans, Engrish, and oddly re-styled NPCs. The servers for that particular version of the game, however, were shut down a few months to a year ago however.
If the game had a LAN option instead of relying on dedicated servers I'd have suggested Hamachi or something similar, but... /shrugs.
Apparently the source code for the original game was "stolen", but that happened over a decade ago with nothing happening since thereby suggesting that whoever got a copy of it out of Flagship has decided not to do anything (obvious) with it.
Logic is the antithesis of faith, else why is it that faith defies logic while logic denies faith?