Preheat the oven to 160°C fan/180°C/Gas 4. Line a 23cm × 33cm Swiss roll tin with baking paper. Grease with a little butter and set aside.
Put the egg yolks and caster sugar in a large bowl and whisk until thick and creamy. Sift the cocoa powder over the egg mixture and whisk it in thoroughly. Wash and dry the beaters, then, using a clean bowl, whisk the egg whites until stiff but not dry. Fold a third of the egg whites into the cocoa mixture, then gently fold in the rest until evenly distributed. Pour into the prepared tin and spread gently with a spatula.
Bake in the centre of the oven for 20 minutes, or until well risen and just beginning to shrink away from the sides of the tin. Remove from the oven, loosen the edges with a round-bladed knife and leave to stand until cold. The cake will sink down into the tin and this is fine.
To make the filling, whip the cream with the icing sugar until thick enough to stand in soft, floppy peaks. Remove the redcurrants from their strings by sliding the stalks through a fork. (Keep a couple of the prettier strings whole for decorating the finished cake.) Place a large piece of baking paper on the work surface and gently turn out the cake on to the paper.
Spread the cream over the cake and dot with the redcurrants. Roll up gently from one of the short sides and transfer to a serving plate with the outer edge end face down on the plate in order to present a smooth top. Dust with icing sugar and cocoa powder. Decorate with the reserved redcurrants and cut into thick slices to serve. This is good chilled as well, but dust with cocoa and sugar only after you have taken it out of the fridge and are ready to serve it.