Combine berries, water, sugar and lemon juice in heavy large saucepan. Bring to simmer, stirring occasionally. Strain berry mixture, reserving juices.
Line twelve 5-ounce ramekins with plastic wrap, so it hangs over the sides. Using a 2 ½- inch 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.
To build a pudding, dip 1 round slice into fruit juices and place in bottom of ramekin. Dip 5 bread squares, one at a time, into juices and place around sides of ramekin. Spoon about ½ cup berries into ramekin. 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 ramekin. Repeat assembling the puddings with remaining bread rounds and squares, juices and berries, assembling.
Place the puddings 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.