Sift together the flour and salt into a large bowl. Cream in the butter until mixture resembles fine breadcrumbs. Mix in the sugar and Madeira until mixture becomes stiff. Wrap dough in foil or cling film and refrigerate for 30 minutes.
Preheat oven to 160 C / Gas mark 3.
On a lightly floured surface, knead dough lightly until smooth. Roll out to approximately 3mm and prick all over with a fork. Cut dough into 36 fingers measuring approximately 2x6cm. Place on baking trays. In a small bowl, lightly beat the egg. Brush fingers with the egg and sprinkle each with sugar.
Bake for about 15 minutes or until light golden in colour. Let cool on wire racks. Store in an airtight container.