Ah, my bad!
Unfortunately my HTML5 exports are not working, so I cannot actually test the code, but for Godot 3.0 the OS class might provide the required information. Specifically, these functions seem promising:
print ("Command line args:");
print (OS.get_cmdline_args());
print ("Executable path:");
print (OS.get_executable_path());
print ("Name");
print (OS.get_name());
And it looks like Godot 2.1 has the same functions. I don't know if these will give the URL, but I couldn't find anything and these functions seem the most likely.
It is rather strange there is not a function for this though. It might be worth opening a feature request, assuming one doesn't exist, on the Godot GitHub repository to have this functionality added.
Anyway, my apologizes for misunderstanding and hopefully one of those functions returns the URL.