I received mine after 5-6 weeks. I think it was mentioned in the paperwork as well.
I believe this is to ensure that you do not order the broadband package just to receive the card and cancel the broadband package before the month's up. Which seems sensible.
I applied for infinity 2 today with 2 days left on the Saintsbury's offer. Now it's not installed for another month. Will this deal still be honoured then?
It took about 2 weeks to receive my gift card after infinity was installed, which was relatively quick as it was done a week before Christmas. I needed to sign for it when it arrived.