Preheat the oven to 180°C (160°C fan) / gas mark 4. Line a 20 x 20cm cake tin with baking parchment.
Combine dry ingredients: In a large mixing bowl, whisk together the self-raising flour, light brown sugar, caster sugar, ground ginger, and mixed spice.
Prepare wet mixture: In a separate bowl, beat the eggs with the vanilla extract. Stir in the yoghurt and vegetable oil until well combined.
Mix wet and dry ingredients: Pour the wet mixture into the dry ingredients. Stir until just combined.
Fold in fruits: Gently fold in the chopped rhubarb and blueberries, ensuring even distribution.
Transfer to tin: Pour the batter into the prepared cake tin, smoothing the top with a spatula.
Add topping: Sprinkle the rolled oats and demerara sugar evenly over the surface of the batter.
Bake: Place the tin in the preheated oven and bake for 40–45 minutes, or until a skewer inserted into the centre comes out clean.
Cool: Allow the cake to cool in the tin for 10 minutes, then transfer to a wire rack to cool completely.
Serve: Slice and serve with a dollop of natural yoghurt and a handful of fresh berries, if desired.