when living in london for a semester should i change plans or just rent a phone locally?
Get a local SIM and use your iPhone (if you have iPhone 5 or greater. 4S can be used too, if unlocked before you left)
What Weth said. Or stay on wifi while there. Cellular data will kill your wallet. Turn off "push" for email. Just turn Cellular off! LOL
I'd actually go even further and call Verizon and have the data plan turned off while you are living in London. That way there are no mistakes. You can run up data charges quickly if the data becomes turned on either on purpose or inadvertently. Wifi will still work.