Just applied for mine and the email that sent to me says 45 days wait.
i rang them and got a email to say it would be with me within 15 working days which was about 25 working days ago , so emailed them still no gift card ,
I had my Broadband installed on 11/10/2013, I filled out the forms for my Sainsburys giftcard on 22/11/2013. Therefore it has now been over 70 days since installation and over 50 days since I filled in the forms.
I tried to contact BTCare on Twitter who had me fill in a form with my details and said they would contact me as soon as possible, this was two days ago and I've heard nothing. I've tweeted them again since and I've replied to the email confirming they had recieved my complaint, but still no contact.
I already had a ton of problems prior to installation with BT (cancelling engineer visits hours before they were due, engineers simply not turning up, waiting 45 minutes on the phone to customer services just to be told there was nothing they could do, my installation would have to be delayed by two weeks) so I am getting pretty fed up of being ignored and left in the dark now. The actual services (phone and broadband) are great but your customer service leaves a lot to be desired.