For the filling, put the blackcurrants in a small saucepan with the sugar and 3 tablespoons water. Bring to a simmer and cook for 5–7 minutes until the berries are completely soft. Blend to a purée and push through a sieve to remove any seeds. Leave to cool, then chill.
Heat the oven to 180°C/Fan 160°C/Gas 4. Lightly brush the base of a Swiss roll tin with the oil. Line with baking parchment. Using an electric mixer, whisk together the eggs and sugar for about 5 minutes until pale and creamy and doubled in volume. Sift half of the flour on top and gently fold in using a large metal spoon. Repeat with the remaining flour and fold in until there is no flour visible. Finish by folding in 1 tablespoon warm water, which helps give a lighter airy sponge when cooked.
Pour into the tin, lightly spreading into all of the corners. Bake for 10–12 minutes until lightly golden and springy to touch.
Cut a piece of baking parchment slightly bigger than the sponge and dust heavily with sugar. Carefully and swiftly turn the cooked sponge upside down onto the sugared surface and carefully peel away the lining parchment from the top. Cover with a clean tea towel to keep the sponge moist and leave it to cool completely.
Whisk together the cream and elderflower cordial until it starts to form peaks. Stir in the purée and spread over the cooled sponge, leaving a 2cm border. Starting at one long edge of the sponge, gently roll the sponge away from you into a log shape, ending with the seam underneath. Serve sprinkled with sugar.