Preheat the oven to 160°C (fan 140°C), or gas mark 3. Grease and line a 20cm/8in round tin.
Cut the butter into pieces and drop into a medium pan with the honey and sugar. Melt slowly over a low heat.
When liquid, increase the heat under the pan and boil for about one minute. Leave to cool.
Beat the eggs into the cooled honey mixture using a wooden spoon. Sift the flour into a large bowl and poor in the egg and honey mixture, beating until you have a smooth batter.
Pour the mixture into a tin and bake for 50 mins - 1 hour until the cake is well-risen, golden brown and springs back when pressed.
Turn the cake out on a wire rack.
For the topping, cream together the icing sugar, butter and ginger syrup. Spread over the cake when cool.