This used to happen to me, im on giffgaff, i told them to add the Mobile Internet Bar on my account (this would mean you can only connect to internet via Wifi), you can have it removed when you want (by asking them), i used to get charged all the time (even when having mobile packet data and background data turned of), i dont think you can put the mobile internet bar on with o2, but you can with giffgaff (and giffgaff is great; goodybags, payback etc), i would recomend giffgaff to you, go here to order a free sim with £5 free credit on it
: Order a Giffgaff sim and you will get £5 free credit when you activate it:
https://giffgaff.com/orders/affiliate/mohy