I wanted a thicker consistency as this makes icing the cakes significantly easier. Start with a large amount of icing sugar and gradually add small drops of water until you can stir the mixture but with some degree of resistance.
Dollop a small amount of the icing into the centre of the cake and spread it, moving the spoon or palette knife in circular motions. Do this until a circle of icing is formed that spreads to nearly the edge of the cake, leaving a small space around the outside. If the icing is the correct consistency, it should naturally spread to the very edges of the caking. Leaving the icing to do this of it's own accord creates a much neater, less forced-looking edge and a smoother surface. Once iced, leave the cakes in room temperature until the icing sets. I suggest you choose one that's worked slightly less well as a 'tester cupcake'. This means you can test the solidity of the icing with your fingers without worrying about leaving dents on the 'better looking' examples.
I also added a drop of lilac food dye to give it a bit of colour.