Just chiming in. I got a GOG copy to support GOG and try this mod, and what happened was the same to me.
Fallout London starts, then when you click "New game" you get a graphic and it freezes within a second, and freezes to the point where for me, I have to restart my computer.
Attempting to start a new game in FO4 with no saves on my computer, no ini files, nothing, and I just get the infinite loading screen where the graphic is cycling but it never loads in.
I had no choice but to refund the GOG version after reinstalling Steam's version, loading into my game within 5 seconds, and also being able to start a new game.
Not sure why the GOG version is having these issues. There should be no problems, comparatively speaking.
It is what it is though. At least I have my copy of Alone in the Dark to show my support for the GoG team...