Preheat oven to 180 C / Gas 4. Butter six ramekins and place in a roasting tin.
Mix blueberries, lemon zest and 2 tablespoons caster sugar together in a small bowl.
Microwave 2 tablespoons butter in a microwave-safe bowl until melted, about 30 seconds. Stir in brown sugar. Spread equal amounts into the bottom of each ramekin. Divide the blueberry mixture evenly into the ramekins.
Beat 120g unsalted butter and 100g caster sugar in a large bowl using an electric mixer until fluffy. Add eggs 1 at a time, mixing after each addition. Mix in lemon juice and vanilla extract. Add flour, baking powder, ginger and salt; stir until combined. Mix in milk. Spoon cake mixture into the ramekins over the blueberry mixture.
Bake in the preheated oven until a skewer inserted into the centre comes out clean, 25 to 35 minutes.
Let cool in the ramekins for 5 minutes. Run a knife around the edges of the cakes; turn out onto a plate.
If the cake mixture looks too dry, add in a little milk at a time until the desired consistency is reached.