An itemised bill should make it clear what you've been charged for.
If they promised something and then didn't deliver, you should explain things in writing stating that the bill is disputed with your full reasons. Any important correspondence should be sent by recorded delivery.
It is possible that BT will want to push you into paying with red letters and threats of disconnection. How far you want to dig your heels in is up to you but you could, if you wanted to take things that far, suggest that failing any other agreement you would be willing for the matter to be put before a magistrate for him/her to decide.
You need not be paying more than 2p per minute for calls to New Zealand if you Google for "cheap international calls" and it might be worth looking into something like this until everything has been clarified by BT.