It takes about a week from when they tell you they sent them. However, you placed your order in the Christmas period, and I would expect them to be closed on the 26 & 27th (at least!), and January 2nd, so they have only had your order for 4 working days. It usually takes about a week to get the pickups made, so I think that you still will need to wait a few days before they send you an email.
The English holidays over Christmas are much bigger than the US ones, and a lot of people take the whole week off between Christmas and New Year. Not sure if that is the case at BK, but I am sure someone will let you know once they get in today.