I know that this won’t help anyone, but I’ve managed to redeem the offer successfully via the link in MyBT.
I've completely given up now.
I got a new email link today from BT via an email saying it was a last chance thing and this time it worked with that link embedded in the email.
I spoke to BT this morning who promised me an email would be sent later on today which would resolve the issue. As per @Brookstermax post earlier today, the email contains a link to the Athletic which actually works.