Preheat your oven to 180C / 350 F / Gas mark 4 and either very lightly grease or line two 8 inch (20 cm) tins and place them to one side.
In a large mixing bowl with a wooden spoon or electric hand mixer or using your stand mixer cream the butter and sugar together until they are very light and fluffy.
Add in the lime zest and juice and cream everything together. Then add the eggs one at a time mixing well between each addition.
If the mixture splits don't worry, just take a teaspoon of your flour and add it in and it should come back together. Sometimes this happens but don't panic your cake is not ruined. A little flour will sort it out.
Add your flour and baking powder to the bowl and by hand gently fold it in to the batter using either a metal spoon or a rubber spatula. Be careful not to knock out all the air.
Divide the batter evenly between the tins and smooth the tops and pop them in the middle of your oven for 25 minutes.
Resist temptation to open the door before this otherwise your cake may sink. Once 25 minutes are up check to see if your sponges are golden brown and springy to the touch.
If they are take them out of the oven and allow them to sit in their tins for at least five minutes then turn them out onto a cooling rack to fully cool down.
While the cake is cooling it's time to make the buttercream. Beat the butter till it is very pale and fluffy. Add in the lime zest and juice and mix until well distributed.
Add in the icing sugar and mix until you have a pale buttercream.
When the sponges are cool place one half on your serving plate and spoon the blueberry jam onto it, spread until it is almost at the edges and then sandwich the two halves together.
Spoon your buttercream on the top and spread it all over the top of the cake. Cut and serve!
This cake needs to be kept in an airtight tin at room temperature. It should keep for up to 5 days.