Photograph: Maja Smend
Preheat the oven to 170°C, fan 150°C, gas 3. Grease and line a 18cm x 28cm rectangular tin with baking paper.
Tip all of the cake ingredients into the bowl of a mixer and beat for 2 minutes, until smooth. Pour the batter into the prepared tin and level with a palette knife.
Bake on the middle shelf of the preheated oven for about 40-45 minutes, or until well risen, golden and a skewer inserted into the middle of the cake comes out clean.
Meanwhile, make the Pimm's syrup. Put the Pimm's and caster sugar in a small pan over a low heat, and stir to dissolve the sugar. Once the sugar has dissolved, increase the heat and bring to a boil. Boil for 7 minutes until syrupy and reduced by half, then pour the syrup into a small measuring jug.
Using a skewer, poke holes all over the warm cake, then pour 100ml of the syrup over and leave the cake to cool completely on a wire rack. Set aside the remaining syrup.
Now make the buttercream. Place the egg whites and caster sugar into a large, heatproof bowl over a pan of simmering water – ensuring the water doesn't touch the bowl. Using an electric whisk, whisk until the sugar dissolves in the egg whites. Test by rubbing some of the mixture between your thumb and index finger – you shouldn't be able to feel any sugar granules, and it should feel warm. Take the bowl off the pan and continue to whisk for 3-4 minutes on high speed. The bowl should be cool to touch at the end of this. Ensure the bowl is cool enough for the butter not to melt when you start adding it to the meringue.
Reduce the speed to medium and start adding the butter, one piece at a time, allowing each cube to be incorporated before adding the next. After half the butter has been added, the mixture may look curdled. But keep adding the butter and the buttercream will come together. This will take around 4-5 minutes. Continue to whisk until the buttercream is light and fluffy. Then add the Pimm's and chopped mint to taste.
Cover the top of the cold cake with the prepared buttercream. Toss the oranges, strawberries and cucumber with the remaining Pimm's syrup and sprinkle over the top of the cake with the extra mint leaves just before serving.
Warning: this recipe contains partially cooked eggs.
Get ahead: make up to the end of step 5 up to a day ahead. Store in an airtight container.