Pull the redcurrants from their stalks, if necessary, by running them between the tines of a fork. Mix with the raspberries and mash very lightly.
Place 16 mini silicone muffin cases on a baking sheet.
Sift the flour and baking powder into a bowl and stir in the sugar. Beat together the yogurt, egg, vegetable oil and vanilla extract and stir in the fruits. Add to the dry ingredients using a large metal spoon, stir the ingredients together until only just combined. Divide among the cases.
Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for about 10 minutes until risen and firm. Leave in the cases for 2 minutes, then transfer to a wire rack to cool. Dust each muffin lightly with icing sugar.