Preheat the oven to 190C/375F/Gas 5. Grease and line a 20cm/8in square cake tin.
Beat together the butter and sugar in a bowl until light and fluffy. Beat in the eggs, a little at a time, until well combined. (If the mixture looks like it is curdling add a spoonful of the flour.) Fold in the flour and add a little milk if the mixture looks stiff.
Spoon the cake batter into the cake tin and level using the back of a spoon. Bake for 35-40 minutes, or until golden-brown and a skewer inserted into the middle comes out clean.
Remove the cake from the oven, set aside to cool for 5 minutes, then turn out and allow to cool completely, upside down, on a wire rack.
Meanwhile, for the sugar syrup, heat the sugar and water in a saucepan until the sugar has dissolved. Stir in the lemon essence.
For the filling, beat the butter in a bowl until soft and smooth, slowly beat in the icing sugar. Continue to beat until fluffy.
Very carefully, using the longest knife you have, remove the dark crust from the top of the cake and turn the cake upside down. Then cut the cake in half horizontally.
Drizzle or brush the bottom cake layer with the sugar syrup and then spread with the buttercream. Top with the jam and carefully sandwich with the top half of the cake.
Wrap the cake in cling film and chill for 2-3 hours, this will make it easier to cut the cake later.
Lightly dust the work surface with icing sugar and roll out the marzipan to the same size as the cake. Once the cake is chilled, brush the top of the cake with the sieved apricot jam. Carefully lift the marzipan onto the cake, smooth it flat along the top of the cake and cut off any excess marzipan. Cut the cake into equal 25 x 4cm/1½in squares.
Sieve the fondant icing sugar into a small bowl and stir in enough hot water to make a smooth icing thick enough to coat the cakes. Reserving three tablespoons of the icing into two bowls, cover with cling film and set aside.
Coat the cake squares with the icing, easing the icing down the sides of the cakes until you have an even coating all over the cakes. Sit the cakes on a cooling rack until the icing is set.
Add a few drops of blue food colouring to one of the bowls of icing, mix to a smooth paste and spoon into a piping bag with a very fine nozzle. Repeat with the other bowl of icing using the red food colouring.
Use these two colours to pipe the union jack onto the fondant fancies. Be as simple or as intricate as you dare! Carefully remove the cakes from the rack and sit in paper cases.