I have invited several new players to Fallen London, but have done so off site and had to connect with them after they created an account.
I could see from a forum and wiki search that there used to be ways to invite new players through in-game means, which carried mechanical benefits (perhaps making you already connected with the new player, and possibly material rewards?). The content I did dig up appeared to be retired though.
Is there currently any remaining way to do this in game? Having friends to play with is its own reward, but it still would be nice to get a little something for bringing Failbetter players and revenue.