Cream the butter and sugar in a medium bowl until well mixed and gently glossy. Add in the egg and mix in so well combined.
Add the flour, salt, cinnamon, allspice, nutmeg and lemon zest, if using, and mix together so everything is well combined. The dough should be on the drier side, but still come together - if it seems too dry, you can add a splash of milk but I don't fine it needed. Fold in the currants and mix through so relatively evenly distributed.
Bring the dough together into a flattened ball/disc and wrap in a freezer bag or cling wrap/film. Refrigerate for around 30 minutes to allow the dough to firm up a little more before rolling.
Preheat oven to 350F/180C. Line a couple of baking sheets/trays with silicone mats or parchment paper.
Roll out the dough on a lightly floured surface to around 5mm (¼in) thick. Use a fluted round cutter that's around 7cm (2 ¾in) in diameter and cut out as many as you can - if you don't have a fluted cutter, a plain round will be fine. Once you have cut as many as you can, bring the leftover dough into a ball, roll out and cut out more. Try not to re-roll too much as you will likely get part currants in the leftovers rather than whole ones and the dough will get softer so harder to roll, but still try to use up the dough.
After rolling, transfer the biscuits/cookies to the lined baking sheets. Leave slight gaps between them but they don't spread as they bake so the gaps don't have to be big.
Bake the cookies for around 10-14 minutes until the cookies look dry and are just starting to brown on the base and edges. Immediately as you take them out of the oven, sprinkle over additional fine sugar to give a thin layer over each biscuit/cookie (you need to do this while they are still hot or the sugar doesn't stick). Don't worry if some areas have a little too much, you can shake off any excess once they cool. Leave to cool before gently shaking off any excess sugar - store at room temperature in a sealed container.