There is a fix. Go to task manager, processes, close off the process tree for league, then reopen league and log in. it will send you straight to the loading page and have no issues. If your computer is fast enough it'll have you back into league before the minions spawn, if not then shortly afterwards.
I believe this is actually an issue with some firewalls. I run comodo and despite setting up the rule every time i update lol, it still blocks everything and comes up after the game has already tried to connect (thus the network problem), and then asks whether i will allow it. I think it might have something to do with the file being named slightly differently each patch, but i have tried turning my firewall off to test if the issue still came up and it didn't.
Note: I am not a programmer nor a network support so while this works, I cannot say for sure whether this is the reason for the issue or not, only that this fix has worked for me for the last year :P