Preheat oven to 180 C / Gas 4. Grease two 12-hole tins or line with paper cases.
In a medium bowl, stir together the flour, bicarb, baking powder and salt. In a separate bowl, beat the sugar, melted butter, egg, vanilla, milk and lemon juice with an electric whisk until smooth. Pour in the dry ingredients and mix by hand just until blended. Stir in the rhubarb. Spoon the cake mixture into the prepared cupcake cases, filling 3/4 full.
Bake in the preheated oven until the tops of the muffins spring back when lightly pressed, about 25 minutes. Cool in the tins for at least 10 minutes before removing to cool completely.
For the icing: cream together the cream cheese and butter until light and fluffy. Mix in the vanilla, then gradually stir in the icing sugar till desired consistency is achieved.