Trim the crusts from the white sandwich bread and cut some slices into triangles and rectangles so they will neatly fit and overlap inside a 1.5-quart bowl; set the prepared slices aside.
Gently rinse and drain the raspberries, blackberries, redcurrants, blackcurrants, and strawberries, then place them in a medium saucepan with the granulated sugar, water, and fresh lemon juice.
Bring the pan to a gentle simmer over medium heat and cook, stirring once or twice, 3–5 minutes until the sugar dissolves and the berries release juices but still mostly hold their shape; remove from the heat and cool 10 minutes.
Set a fine sieve over a bowl and pour in the fruit mixture to collect the juices; transfer the fruit to a separate bowl. Measure and reserve 0.5 cup of the collected juices for finishing; keep the remaining juices for assembly.
Line the bowl with the prepared slices, slightly overlapping and pressing to fit so there are no gaps, leaving a piece to use as a lid.
Spoon half of the fruit into the lined bowl and press gently to compact. Add the remaining fruit, then pour in enough of the remaining juices to thoroughly moisten the bread without flooding the bowl. Top with the remaining prepared slice(s) to seal, pressing lightly.
Cover the surface with plastic wrap, set a small plate directly on top, weight with a can or jar, and chill 6–12 hours (8 hours ideal) until the bread is uniformly stained and the pudding feels firm.
To serve, run a thin knife around the edge, invert onto a rimmed plate, and brush any pale spots with the reserved juices. Slice into wedges and serve with heavy cream, lightly whipped.