Aha, I've found Georgio Locatelli's eggless chocolate cake (devised for his allergic daughter):
450g plain flour
6 tbsp unsweetened cocoa powder
2 tsp baking powder
2 tsp bicarbonate of soda
300g caster sugar
125ml vegetable oil
300ml water
2 tbsp distilled white vinegar
2 tsp vanilla extract
Sift all dry ingredients together; mix wet ingredients and add. Beat until smooth. Pour into an oiled 23cm cake tin and bake at 180C for 1 hour. Leave to cool before slicing in half horizontally, if you want to fill the cake with a vegan icing.