It will be iMessage causing this as well as that also requires activation.
This must be a new thing as I was never charged for any FaceTime/iMessage set-up charges when I was on T-Mobile or since I switched to 4GEE. I know Vodafone do (or at least did) charge for these ghost set-up texts but as far as I'm aware EE don't, so it sounds like an error to me.
Do you get a message along the lines of 'please note your carrier may charge for this...' when you turn on either FaceTime or iMessage? If not then something is clearly wrong as you always get a warning message if the carrier charges you for the activation texts.
What iOS version are you using and what EE carrier file version are you using?