There's no need to take the stalks off the blackcurrants, just pile them, about one third of a pound (5 oz/150 g) at a time, into the sieve set over a mixing bowl, and mash like mad with a wooden spoon until you have extracted all the pulp and only the stalks, pips and skins are left in the sieve.
Now place the sugar and 5 fl oz (150 ml) water in a saucepan over a medium heat, stir until all the sugar crystals have dissolved, then let it come to the boil, and boil for 3 minutes exactly.
Then remove from the heat and stir the syrup into the fruit pulp. Whip the cream until it just begins to thicken. Be careful not to overwhip: it mustn't be thick, just floppy.
Fold the cream into the fruit mixture until thoroughly blended. Pour it into the polythene box, and freeze in a freezer or in the ice-making compartment of a fridge turned to its coldest setting.
As soon as the mixture begins to set (after about 3 hours) turn it out into a bowl and beat thoroughly. Then return it to the freezer (in the box) until set – about another 3 hours.
Remove to the main part of the fridge about an hour before serving.