Same here, ordered the pre-paid pure Visa card over 30 days ago, it has not arrived. It was the same with the Sainsbury's gift cards, many people did not receive them after they filled in the standard claim form so they had to use the "contact us" system to actually get one.
They have a special form for it, which is presumably very busy: https://bt.custhelp.com/app/contact_email/c/6090
The cynic in me thinks BT just wait for the secondary claim in the hope people forget they claimed for it over 30 days ago and did not receive it, in order to save themselves some money.
I used the contact form to complain and the support agent simply resubmitted the same form I used over 30 days ago and said I should wait another 30 days.
Mine came on the 30th day - you get an email the week before telling you it is on the way. Had a free shopping trip to Aldo with mine 😉
Useful info about the dispatch email, thanks. I've had no such email as yet. I might have to do this all again for a third time in 3 weeks time. Actually I'll probably just raise a complaint instead.