Preheat the oven to 180 C / Gas 4. Grease baking trays or line with baking parchment.
Sift the plain flour into a bowl and add the baking powder, cayenne and sugar. Rub in the butter and then add the anchovies and Cheddar cheese to form a dough. Using floured hands, divide the dough into two balls and roll both into 4cm (1 1/2 in) logs. Wrap in cling film and chill on a flat surface in the freezer for 10 minutes.
Remove logs from the freezer. Using a sharp knife, slice off discs as thinly as possible. Arrange fairly close together on the prepared baking tray and sprinkle with Parmesan cheese.
Bake the biscuits for 7 to 8 minutes, until light brown and crispy. Remove from the oven and gently transfer the biscuits to a cooling rack. Allow to cool completely before serving.