Preheat the oven to 190 C / Gas 5. Lightly grease a muffin tin or line with paper bun cases.
Cream together cream cheese, sugar and 4 tablespoons butter. Beat in eggs, one at a time, until completely incorporated. Add milk, lemon juice and vanilla; beat until smooth.
Combine 225g flour, baking powder, baking soda, salt and 1 teaspoon cinnamon; stir into cream cheese mixture until just moistened. Fold in apples and bran flakes. Spoon mixture into prepared muffin tin, filling each cup about 3/4 full.
To make streusel topping: rub together brown sugar, 1/2 teaspoon cinnamon, 1 tablespoon butter and 2 tablespoons flour. Sprinkle on top of muffins.
Bake in the preheated oven until a skewer inserted into the centre of a muffin comes out clean, 20 to 25 minutes. Cool in the tin for 5 minutes, the remove to a wire cooling rack.