Pokemon Go works fine on my phone/network (Samsung, EE) but we're having problems with my son's iphone 5c, O2. Quite often it doesn't connect or loses connection to the game, or an error message will state "Safari can't open the page because the server cannot be found".
I went to the O2 store who just sort of shrugged their shoulders but I'm paying for 30gb data per month specifically so my son can play this game and also listen to You Tube - which also causes similar problems.
Seems fine when we're at home using wifi.