http://www.bt.com/includingyou/bt-basic-what-you-get... Yet she is/was (?) getting BT Privacy and Caller Display included for no extra cost and I can not find anything about that in the rather sparse T&C's for BT Basic.Despite there being no minimum contract period for BT Basic, your aunt would have had a contract for BT Basic before this episode. The as yet unanswered question is what the change(s) are.
The usual position with amending a contract is that the existing contract is amended by a new contract. Free BT Privacy and Caller Display in return for a new minimum period of 12 months could meet the requirements for a contract. Any conflicts between the existing and new contract resolve in favour of the new contract, as they would be part of the changes agreed on.
As I said in an earlier reply, any term is only included in the contract if the accepting party had sufficient chance to be aware of it before agreement was reached, and particularly onerous terms are only included if explicit steps were taken before agreement to draw it to the agreeing party's attention.
Certainly a change from BT Basic to standard line rental would appear to be particularly onerous: it's withdrawal of a considerable discount. If free Privacy and Caller Display is not available on BT Basic, but BT offered it by mistake, that's their lookout.
There's a further complexity in the contractual situation - it might be that the "offer" on the phone was an invitation to treat, your aunt's "agreement" was an offer on the terms of the invitation to treat, and BT will subsequently come back with written agreement to that offer. In this case, if the agreement was posted, it is valid from the letter being posted, not it being received.
I still think it more likely that BT made the offer and your aunt accepted that offer, forming a contract for amendment at that point - but it is somewhat sensitive to the facts.
My thinking was to contact BT, requesting escape from the amendment contract under the Distance Selling Regulations if a contract was formed on the phone, or, alternatively, withdrawing the offer made if the "agreement" on the phone was actually an offer. That would return the situation to the unamended contract.
This saves all the hassle of proving what was or wasn't agreed. If Privacy with Caller Display in return for a new 12 month minimum period is available on BT Basic, your aunt can then take out a new amending contract on those terms.