Make a syrup by stirring the sugar with the boiling water until dissolved, then steep the mint sprigs in it until cool, about 15 mins. Discard the mint.
Cook the blackcurrants in the syrup with the glucose for about 5 mins until the fruit is soft. Whizz in a food processor, then strain into a bowl through a sieve (not nylon), rubbing with the back of a ladle or spoon to remove the pips. Stir in the lemon juice and cool.
Freeze in an ice-cream machine according to manufacturer's instructions until it becomes a thick slush, then scoop into a freezer container and freeze. Or pour into a shallow freezer container and beat 3 or 4 times as it freezes. Before serving, allow to thaw and soften for about 10 mins, then serve with sprigs of fresh mint.