I wish I could recommend the Catholic Shrine Cafe, but I cannot. There is no wifi, the food is not top drawer (understatement), and they do not accept swipe cards. Cards need to be used in Walsingham as there is no ATM in the entire village.
The Norton Cafe in the Anglican Shrine has all three, and God bless them for wanting to serve pilgrims.
Also, I want to highly recommend The Pilgrim Shop, which is also online at this address. http://www.pilgrimgifts.co.uk/
I have known the proprietor for three years, and he loves to go out of his way to serve his customers. One of the great beauties of his shop are Spanish lace mantillas, and gorgeous hand-made icons.
Take a peep.
God bless you all on this sunny but cold day from Norfolk.