Preheat the oven to 180 degrees/gas mark 4. Cream the butter and sugar together in a mixing bowl. Add the eggs and the flour gradually, folding as you go.
Split the mixture into two separate bowls, with approximately half the mixture in each.
In one bowl, add the vanilla, and in the other, add the cocoa powder. Mix both well.
Spoon each mixture alternately into a 20cm lined tin, until each is used up.
Using a cake tester, swirl the mixtures together slightly. Make sure the mixture is levelled out (give it a gentle wiggle), then bake for 50-55 minutes.
While the cake cools, melt the milk chocolate and white chocolate (I placed them in the microwave for 30 seconds or so, checking and stirring regularly). Using a teaspoon, drizzle the chocolate onto the cake, one at a time, to create a marbled effect. Leave to set and enjoy.