Separate the redcurrants and blackcurrants from their stalks by holding the tip of each stalk firmly between finger and thumb and sliding it between the prongs of a fork pushing the fork downwards, so pulling off the berries as it goes. Rinse all the fruits, picking out any raspberries that look at all musty.
Place the fruits with the sugar in a large saucepan over a medium heat and let them cook for about 3-5 minutes, only until the sugar has dissolved and the juices begin to run – don't overcook and so spoil the fresh flavour. Now remove the fruit from the heat, and line the pudding basin with the slices of bread, overlapping them and sealing well by pressing the edges together. Fill in any gaps with small pieces of bread, so that no juice can get through when you add the fruit.
Pour the fruit and juice in (except for about two thirds of a cupful), then cover the pudding with another slice of bread. Then place a small plate or saucer (one that will fit exactly inside the rim of the bowl) on top, and on top of that place a 3 lb or 4 lb (1.3 kg or 1.8 kg) weight, and leave in the fridge overnight.
Just before serving the pudding, turn it out on to a large serving dish and spoon the reserved juice all over, to soak any bits of bread that still look white. Serve cut into wedges, with a bowl of thick cream on the table.