I installed London One-click Edition v1.02 (setup_fallout_london_v1.02_iv2.33r7_(64bit)_(76960).exe) clean on Windows 7 SP1 x64 without any previous Fallout 4 installation but it did not work.

Here is a guide to get it working.

- If you have an active Fallout 4 installation and want to keep the settings and save games backup these folders:
%LOCALAPPDATA%\Fallout4
%USERPROFILE%\Documents\My Games\Fallout4

- Install London One-click Edition v1.02

- Delete these folders
%LOCALAPPDATA%\Fallout4
%USERPROFILE%\Documents\My Games\Fallout4

- Copy from the game installation folder (<GAMEFOLDER>, e. g. D:\Games\Fallout - London) these folders
<GAMEFOLDER>\__AppData to %LOCALAPPDATA% and there rename the folder __AppData to Fallout4
<GAMEFOLDER>\__Config to %USERPROFILE%\Documents\My Games and there rename the folder __Config to Fallout4

- Open "%USERPROFILE%\Documents\My Games\Fallout4\Fallout4.ini" in a text editor
Go to section [Archive] or create section if it does not exist
Add these entries or replace them if they exist and then save the file
sResourceDataDirsFinal=
bInvalidateOlderFiles=1

- Launch <GAMEFOLDER>\Fallout4Launcher.exe and open Options to configure your settings but do not launch the game via Play

- Exit game launcher

- Run <GAMEFOLDER>\f4se_loader.exe

Now the main menu should should have the game options in white instead of green and the Fallout London logo.
The loading screen screen should also have a white Fallout London logo on the lower right screen instead of the green Fallout 4 symbol.