Place the following ingredients into your bread machine in this order: 2 eggs, butter, 600ml milk, salt, caster sugar, flour, yeast, cinnamon, raisins. Choose the program for "dough".
Once the bread machine signals it is finished, line a baking tray with baking parchment. Flour your hands and place the dough on a floured work surface. Form a cylinder with the dough and cut into about 10 equal pieces. Shape each piece into a ball and place on the baking tray. Cover with a clean damp towel, and let the buns rise until doubled, about 2 hours.
Preheat the oven to 180 C / Gas 4. Whisk together the 1 egg and the 1 tablespoon milk. Brush the buns with the egg wash.
Bake in the preheated oven until a dark golden brown, about 25 minutes. Remove from oven and let cool.
Stir together the icing sugar and just enough lemon juice to make a fairly thick icing. Pour a little icing from the tip of a spoon in the shape of a cross on each cooled bun.