You can stop your iPhone itself from using mobile data however you cannot stop some apps from accessing the internet and not others. But closing any apps that run in the background should help decrease your monthly data costs.
You can check how much mobile data is used by each installed app by going to Settings > Mobile and scrolling down through the different apps. You can monitor and track your mobile data usage by tapping Reset Statistics (at the bottom of the Mobile page) at the start of the monthly charging period, and checking against your monthly data bill.
Sometimes iPhones can be "buggy" and use more data than they should. If this is happening, you can fix it by restoring your phone to factory settings (which wipes the phone clean) after backing up your data and apps to iTunes:
It has been noted by many iPhone users that they have been experiencing increased data consumption with later versions of iOS. This is mainly due to iTunes Match and iCloud syncing. If you are consuming more data using iTunes Match and iCloud syncing, you can turn these off in your Settings.
If you still need help with your iPhone using too much mobile data, contact AskOtago:
Tel +64 3 479 7000 or 0800 80 80 98