Preheat the oven to 200C/180C Fan/Gas 6. Line a 2lb loaf tin.
In a large bowl, or the bowl of a stand mixer, cream together the butter and sugar for 3-5 minutes on high (until the mixture is light and fluffy).
Add the eggs, one at a time, mixing in between.
Add the lime zest and flour (or flour and baking powder if using plain flour) and fold together.
Pour mixture into the lined tin and bake for 40-50 minutes, until golden brown and a toothpick or knife comes out clean when inserted. Use this knife/toothpick to poke several holes in the top of the cake.
Mix the lime juice and granulated sugar together and pour over the cake while it's still warm. Let cool on a wire rack.
Once cool, make the strawberry glaze by smashing the strawberries, adding the icing sugar and milk and combine to form a glaze. Pour over the cake (whilst still in the tin).
Optional: decorate with lime zest and strawberry slices.
Let the glaze set before removing the cake from the tin. Slice and serve.