Line a baking sheet with baking paper and have it standing by alongside a large basin of iced water. Cube up the butter. Lightly toast the coconut until golden.
Put the sugar and glucose in a medium-sized heavy-based pan with 2 tablespoons of water. Pop in a sugar thermometer and heat gently over a medium heat, until the sugar has melted and begins to caramelise.
Once it reaches 150ºC, remove from the heat and quickly set it in the basin of iced water to halt the process. Immediately remove and whisk in the butter until incorporated. If it begins to separate, place back on the heat and continue to whisk and emulsify.
Using 2 tablespoons, drop spoonfuls of the toffee onto the lined tray. Sprinkle immediately with the desiccated coconut. To make lollipops, press the sticks into the toffee now, almost all the way across the discs, so that they hold in place.
Set aside to cool and harden. Store between sheets of greaseproof paper or cellophane in a sealed container and eat within 10 days.