Roll out the pastry on a lightly floured surface and use to line a greased 23 cm (9 inch) square shallow baking tin or small roasting tin. Line the pastry case with greaseproof paper and fill with baking beans (or dried beans reserved for the purpose). Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 15 minutes. Remove from the oven and remove the paper and beans. Reduce the oven temperature to 180°C (350°F), Gas Mark 4.
Beat together the butter, sugar, flour, baking powder and eggs in a bowl until pale and creamy. Spoon over the pastry base and level the surface. Arrange the figs over the top. Bake in the oven for about 45 minutes or until risen and golden. Leave to cool in the tin.
Make the icing. Beat together the icing sugar and lemon juice in a bowl to make a smooth, spoonable icing. If necessary, beat in a dash of water or extra lemon juice. Drizzle the icing over the cake, then cut into squares or fingers.