Place the butter, salt and sugar into a large bowl and cream together until smooth. Add the plain flour, rice flour, currants and mixed peel and stir together then use your hands to gently knead together until you get a uniform dough.
Preheat the oven to 300F and line a cookie sheet with baking paper.
Roll the dough out to be just less than 1/2-inch thick. Use cutters to cut the dough out. Prick the top of the cookies with a fork. Bake for 25-30 minutes, the cookies will not really brown, they'll just become firm and very slightly golden around the edges.
Let cool on a wire rack then store in an airtight container.