For the filling, prepare the jelly according to packet instructions. Place in a shallow dish so that the layer of jelly is about 1.5cm thick. Place in the fridge to set completely.
Preheat the oven to 180 C / Gas 4. Line a Swiss roll tin (about 29x35cm) with parchment.
In a mixing bowl, beat the egg whites until stiff. Gradually add the sugar and beat till dissolved. Gently mix in egg yolks.
Sift together the flour, cornflour and baking powder, then gradually add to the egg mixture, folding in gently. Finally, stir in the oil and vinegar. Spread the mixture evenly over the prepared tin.
Bake for 15 minutes. It should be springy to the touch.
Lay out a clean tea towel, and sprinkle it with icing sugar. Turn the hot Swiss roll out onto the towel. Roll the cake up in the towel, and leave it to cool.
Puree the strawberries in a food processor or mash by hand. Cream the butter, then gradually mix in sugar and strawberries.
Cut the jelly into long, 1.5cm thick strips.
Unroll the sponge, peeling away the parchment. Spread the filling evenly over the sponge, leaving a 2cm space on one side. Arrange jelly strips one after another in line on the opposite side. Roll the sponge back up, starting with the side containing the jelly strips so that they're in the middle of the cake.
Set aside the Swiss roll, seam down, in a cool place for an hour. Dust with icing sugar or cover with any remaining strawberry buttercream. Cut into slices and serve.
Use pre-made strawberry jelly instead of making your own and waiting for it to set.