Preheat your oven to 180°C (160°C fan, Gas 4). Grease and line a round cake tin.
Cream together the butter and caster sugar until pale and fluffy.
Gradually add the eggs, one at a time, beating well after each addition. If the mixture starts to curdle, add a little flour.
Fold in the rest of the flour, the lemon zest, and lemon juice gently until well combined.
Gently fold in the blueberries, trying not to crush them.
Spoon the mixture into the prepared cake tin and smooth the top.
Bake for about 50-60 minutes or until golden and a skewer inserted into the center comes out clean.
Let the cake cool in the tin for a few minutes, then turn out onto a wire rack to cool completely.
For the icing, mix the icing sugar with enough lemon juice to make a thick but pourable icing. Drizzle over the cooled cake.