I guess you have an I-Phone, I don't know how in-game purchasing works on such devices AFAIK the only way I could end up with charges like that on my EE bill is by those text message things. With Andriod and the Play Store it's linked to your Google account, you can store credit card details against the account but I don't so it wouldnt happen, I'm guessing Apple would have something similar.
Like I said just get them to detail exactly what you've been billed for, that way you can shut it down, don't they text you every month saying your bill is online to be viewed ? Its pretty easy to setup your EE account given its associated with a phone you own, get it done and check you bill every month, it's a jungle out there