I believe I have solved this - and It's a real "You're gonna kick yourself" solution...
- When you can't log into public WiFi ...
- with an iDevice running iOS7…
- because the Server times out ...
- or the login/registration page just won't load ...
********Simply do this***********
- Go into settings> WiFi and tap the little info icon for the network you are trying to join
- If you see two slider buttons, these are the cause of your woes
- One says "Auto Join" (or similar) - you can leave this ON
- The second button is "Auto Login" - you must turn this OFF (slide it left so it is grey not green)
- Now go back and reselect the network.
- If the login page doesn't come up automatically, open a Safari window and enter any address
I have reproduced this issue and solution in 100% of the public WiFi spots which I could previously not access. Please not that I also have "Block Pop-Ups" turned OFF in Settings> Safari, though I do not know if this is a necessary step.
I have filed a bug report with Apple. Feel free to contact them yourselves if this workaround works for you.
Also, please mark this as "Solved" if it works for you so that others will know how to connect to public WiFi.