For most smartphones you can switch off the data connection on the phone itself.
Many Android phones have Mobile Data in the settings menu, accessible when you swipe down
Or on iPhone choose Settings, then Mobile.
For other mobile phones, have a look at our device help guides online for help managing your data connection.
If you want to stop your phone from going on the internet you could use a bar, to do this you’ll need to get in touch. This will stop your phone from being able to access the internet at all.