Preheat the oven to 180C/350F/Gas 4. Grease a deep 20cm/8in tin with margarine.
Purée the diced oranges in a food processor, and set aside.
Cream the margarine and sugar in a bowl until light and fluffy. Mix in the eggs and then add the baking powder and semolina. Stir to combine, then fold the orange pulp through the mixture.
Pour the mixture into the prepared tin, and put into the oven. After the first 10 minutes, turn the oven temperature down to 170C/325F/Gas 3 and bake for a further 40 minutes, or until the cake is golden-brown on top and a skewer inserted into the middle comes out clean.
Remove the cake from the oven, and allow to cool in the tin. Once cool, run a knife around the edge of the tin to release the cake, and then turn out. To serve, cut the cake into 12 slices.