Preheat the oven to 180°C (350°F/Gas 4). Lightly grease a 20cm (8inch) square cake tin and line with baking paper, leaving the paper hanging over the edge of the tin on all sides.
Cream the butter and sugar in a small bowl using electric beaters until light and fluffy. Add the eggs one at a time, beating well after each addition. Sift the flours over the mixture and fold into the mixture with the ginger. Spread into the tin. Arrange the plum halves on top, pressing them in. Scatter with the flaked almonds, pressing in gently, then drizzle with the honey.
Bake for 1 hour 10 minutes, or until firm and golden. Cover the top with foil if the slice starts to brown too much. Cool in the tin, then lift out, using the paper as handles. Cut into pieces. Store the slice for 4–5 days in an airtight container in the refrigerator.