Preheat the oven to 180C/350F/gas mark 4. Thoroughly grease a 10 cup bundt tin.
Cream together the butter, sugar, lime zest and vanilla extract until very light and fluffy.
Set aside 2 Tbsp of the flour then sift together the rest with the baking powder and salt.
Whisk the eggs into the butter mixture one at a time, mixing well after each addition.
Fold in 1/3 of the flour then 1/2 of the buttermilk followed by another 1/3rd of the flour, the rest of the buttermilk then the rest of the flour; it should be very thick.
Toss the berries with the reserved 2 Tbsp flour then tip the lot into the batter and fold through. Dollop the batter into the prepared tin and spread it level.
Bake for 55-60 mins until a skewer inserted into the centre comes out clean and the cake is starting to come away from the sides of the tin. Leave to cool in the tin for an hour then carefully turn it out onto a wire rack .
Drizzle over the syrup (recipe below) then leave the cake to cool completely.
Make the syrup while the cake is in the oven. Place the sugar and lime juice in a small pan over a medium heat and stir until the sugar has dissolved. Bring up to a simmer and leave to cook for a couple of minutes until reduced slightly. Remove from the heat and set aside to cool.
Place the chopped chocolate and the double cream in a heatproof bowl over a pan of gently simmering water, don't let the bowl touch the water. Stir every now and again until the chocolate has melted.
Remove from the heat and gradually stir in the lime juice. Place the ganache in the fridge until it has become thick but still pourable, about an hour.
Transfer the cake to a serving platter and pour over the ganache then serve.