It sounds like the transfer was not done correctly in the slightest.
Was this placed over the phone or in-store?
When doing a BT to EE migration, it should go in the same name as the original account holder as a matter of policy, and the migration system has no way of changing the account holder. The only exception to this is when the BT Broadband is out of contract, as then a new order can be placed under a different name and will take over the existing line, without incurring any early termination fees on the BT account.
This situation is further complicated by the order being placed to the wrong address, which is not the simplest thing to correct.
What they have likely done is set up an entirely new EE Broadband account under your name, and the BT billing system has no way of knowing due to the wrong address being inserted. If the BT account was to be cancelled at this moment in time, you would have no service at your address as the EE is set up elsewhere.
I think it's a case of someone trying to be too smart with the system and instead of using the correct route, which is to migrate the existing BT account under the same account holder or wait until it is OOC to place an EE order in your name, they have instead created made a major headache for everyone.
If you have had no luck escalating it up to now, you should log a complaint here and insert all of the details and steps along the way: https://ee.co.uk/help/contact-ee/complaint/complaint-form
Due to the three separate accounts involved (EE Mobile, EE Broadband and BT Broadband) any solution will be complex. The most straightforward solution is cancellation of the EE Broadband order which was placed incorrectly, but there may be mobile offers with significant discounts linked to this, adding further complexity.
Let us know how you get on with escalating it.
Unfortunately there is no account access on these forums to be able to offer any direct help, just signposting by other users and customers.
