If you are a new customer to BT you become eligible for the gift after 14 days have passed but it can take up to 28 days after that and possibly longer with the current crisis, for the email to be sent to you so you can claim your Xbox from the BT Shop, who will then dispatch it.
Have 28 days passed yet?
I have asked a moderator to provide assistance, they will post an invite on this thread.
They are the only BT employees on this forum, and are based in the UK.
Please bear in mind that with the current crisis, it could take a long time for one of them to deal with your request.