Roughly chop the tomatoes into 2 cm (¾ inch) pieces and put them in a non-metallic bowl. Sprinkle over the sea salt and leave to stand for 1 hour.
Remove the crusts from the ciabatta and tear the bread into rough chunks.
Give the tomatoes a good squash with clean hands, then add the bread, onion, basil, vinegar and oil. Season to taste with salt and pepper. Mix together carefully and transfer to serving plates. Garnish with the drained anchovies and the reserved basil and serve.