I havn't seen anywhere that takes old Christmas cards for recycling. A couple of years ago there were a few places, Tesco, Boots, WH Smith and also the company where I work. Perhaps we are supposed to use our own recycling bins now?
Sainsbury's in Bermondsey Square has had a box for over a week. It is a group-wide scheme, similarly with Tesco. Sometimes one has to ask a member of staff for the location, as Easter Eggs are possibly hiding the box :p