If using fresh yeast, mix the lukewarm milk and water together, add the fresh yeast and stir with a fork until dissolved. If using dried yeast, follow the directions on, then stir in the milk. Sift the ﬂour and salt into a large, warmed mixing bowl and rub in the butter with your fingertips. Mix in the currants and a third of the caster sugar.
Make a well in the centre, pour in the yeast liquid and mix to form a soft dough. Turn out on a lightly ﬂoured surface and knead for 5–10 minutes until smooth and elastic.
Put the dough in a clean, lightly ﬂoured bowl and cover with plastic wrap. Leave in a warm place for 1–1 1/2 hours, or until the dough has doubled in size.
Turn the risen dough out on a lightly ﬂoured surface and, with clenched fists, knock it back to its original size. Divide the dough into eight equal pieces, shape each piece into a neat round and roll out to about 12 cm in diameter. Put the dough rounds on greased baking trays, loosely cover with plastic wrap and leave in a warm place until the dough has risen and doubled in size.
Meanwhile, preheat the oven to 220°C. Bake the teacakes for 20–25 minutes, or until they are golden brown and sound hollow when tapped on the base. While they are cooking, put the remaining caster sugar in a small saucepan with the cold water, stir over medium heat until dissolved, then boil for 1 minute. Remove the teacakes from the oven and brush them with the hot sugar syrup.
You may like to serve the teacakes warm, split in half and buttered. Otherwise, transfer them to a wire rack and leave to cool. Once cool, they can be cut in half, spread with butter, sprinkled with the cinnamon and sugar mixture, and then toasted, if desired.