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Settings-power management,wifi by location must be enabled.
But wifi by location might download some data to be able to work. Do you have it enabled?
GPS shouldn't affect your data plan, are you sending or receiving MMS? because if you are then that's the issue as MMS won't go through WiFi.
What if you try to disable wifi by location and see how it is?
Is or was your phone locked to a carrier/network branded? perhaps there's an app that its creating this issue
Boot on safe mode and check again
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008