Heat the oven to 170C (150C fan). Grease a deep, loose-bottomed 18cm cake tin and line the base of it with baking parchment.
Beat the butter and caster sugar together with an electric whisk until pale and fluffy. Add eggs, one at the time, beating well after each addition, then stir in the lemon zest. Fold in the 250g of flour, 1/2 tsp baking powder, 1/2 tsp of salt and 100g Greek yogurt. Mix until the ingredients are JUST combined.
Spoon the mixture into the prepared tin and smooth the top with a spatula. Bake in the centre of the oven for 50-55 minutes, until golden brown on top and firm to the touch. Cool the cake in the tin for 10 minutes, then remove from the tin and cool on a wire rack completely.
Sieve 400g of icing sugar into a bowl and beat in enough of the lemon juice to create a thick icing. Set the cake on a cake stand or a plate and spoon over the icing, allowing it to drip down the sides a little.
Peel large, wide strips from 2 large lemons using a vegetable peeler. Remove any white pith with a sharp knife, then julienne the peel into very thin matchsticks. In a small saucepan, add the granulated sugar and water and set it over a medium heat until the sugar has dissolved. Add the lemon peel and simmer gently for 15 minutes then scoop the peel with slotted spoon and set on a paper towel to cool. Use to decorate the cake with it.