Place the sugar and water in a saucepan. Stir over low heat until the sugar has dissolved, then bring up to the boil. Wash the mint leaves and squeeze dry. Place in a blender. Pour in the hot syrup, cover and blend for a few minutes until the mint is very finely chopped. Leave the mixture until quite cold, then strain into a mixing basin.
Add the strained juice of the lemon half and stir in the double cream. Whisk lightly to blend the ingredients and add a little green food colouring if liked. Pour into a large refrigerator ice tray or a polythene freezer box. Cover and place in the freezer. As the mixture becomes icy round the sides, turn the edges into the centre with a fork. When the mixture is half frozen turn out into a chilled basin and give it a really good mix. Return to the container and refreeze. Leave for several hours until quite firm.
Before serving, remove the container to the refrigerator compartment for about 30 minutes before serving, to allow the ice cream to soften slightly.