Combine berries, water, sugar and lemon juice in heavy large saucepan. Bring to simmer, stirring occasionally. Strain berry mixture, reserving juices.
Line twelve clear decorative bowls with plastic wrap, so it hangs over the sides. Using a round cookie cutter, cut out 24 rounds from bread slices. Trim crusts from 16 remaining bread slices and cut each slice into 4 equal squares
Dip 1 round slice into fruit juices and place in bottom of bowl. Dip 5 bread squares, one at a time, into juices and place around sides of bowl. Spoon about ½ cup berries into bowl. Dip 1 more bread round into juices, place on top of the berries and wrap with the plastic wrap hanging over the sides of the bowl. Repeat assembling the puddings with remaining bread rounds and squares, juices and berries, assembling.
Place the bowls on a baking sheet. Top with another baking sheet. Place a heavy object on baking sheet (this extracts more juices and pectins to set the puddings). Chill overnight.
Combine any remaining berries and juices in bowl; cover and chill and serve with pudding if desired.
To serve, unwrap puddings. Turn out onto plates and remove plastic wrap.