Preheat the oven to 175°C (fan-assisted).
Beat the butter with the sugar and vanilla until light and creamy. Add the eggs one at a time, mixing well after each addition.
Sift together the flour and baking powder.
Gradually add the dry ingredients to the wet mixture, alternating with the milk. Begin and end with the flour.
Just before baking, add the blueberries to the batter.
Transfer the batter into a piping bag and fill the muffin liners.
Spoon a generous amount of crumb topping onto each muffin, then bake for 25 minutes. Check doneness with a skewer, it should come out clean.
If you're making a large batch, divide the batter into portions and add the fruit only right before baking. Otherwise, the blueberries may bleed into the batter if left too long.