Preheat the oven to fan 180°C/gas 4. Spray a 900g (2lb) non-stick loaf tin with a few sprays of oil.
Using a stand mixer or electric hand whisk and large bowl, cream together the margarine, caster sugar and sweetener until light and fluffy. Add the eggs, one at a time, beating well after each addition.
Sift the flour, bicarbonate of soda and ground cardamom together over the mixture, add the vanilla seeds and lime zest and fold in gently, using a spatula, until just combined. Lastly, fold in the grated courgettes.
Spoon the cake mixture into the prepared tin and gently level the surface. Bake on the middle shelf of the oven for 50–60 minutes. To test, insert a skewer into the middle of the cake: it should come out clean; if not give it a little longer.
Once cooked, leave the cake to cool in the tin for five minutes, then transfer to a wire rack to cool completely.
To make the icing, in a bowl, whisk the icing sugar, cream cheese and lime juice together until smoothly combined.
Spread the icing on top of the cake and sprinkle with the lime zest. Cut into eight thick slices to serve.