Preheat the oven to 180°C/160°C fan/350°F/gas mark 4. Grease a 23 cm/9 in square cake tin and line it with baking parchment.
Sift together the plain flour, cornflour, baking powder, bicarbonate of soda and salt in a large bowl.
In a jug, whisk together the non-dairy milk, non-dairy yogurt, melted vegan butter, oil, sugar, vinegar and vanilla extract until they are very well combined.
Pour the wet ingredients into the dry and whisk with a balloon whisk until no dry lumps remain. Be careful not to over-beat the batter.
Pour the batter into the prepared tin and spread it level. Bake for about 25 minutes until the cake is firm to the touch and a skewer inserted into the centre comes out clean.
Leave the cake to cool in the tin for 20 minutes then carefully turn it out onto a wire rack. Leave until it is completely cold.
Once the cake is cold, use a sharp serrated knife or cake wire to level the top and trim the edges so that they are straight. Cut the cake into 16 squares.
Slice each square in half with a small, sharp serrated knife and sandwich the two halves back together with a dollop of jam. Spread it almost up to the edges.
Place the cake squares on a baking parchment lined tray and freeze for at least 30 minutes, until firm.
To make the chocolate icing, whisk together the cocoa powder, icing sugar and boiling water in a large bowl. Whisk in the chopped chocolate until melted and smooth. Set aside until it has cooled to about room temperature. Place the coconut in a shallow dish.
One at a time, dip each frozen cake square in the chocolate mixture, making sure that it is completely coated. Use a couple of forks to help you to turn it while keeping your hands clean.
Shake off the excess icing then then roll it in the desiccated coconut until all sides are covered. Place on a wire rack. Repeat with the rest of the Lamingtons. You may wish to keep most of them in the freezer while you work on a few at a time.
Leave the Lamingtons on the wire rack for a couple of hours until set then store in an airtight container.