In a large saucepan, combine the potatoes and enough water to cover. Bring to a boil, salt the water and cook until tender, about 8 minutes. Rinse under cold water, then drain well.
In a large bowl, whisk the lemon juice, the anchovy paste, if using, and the garlic paste. Whisk in the EVOO until thickened. Add the cooled potatoes, the tomatoes, celery, onion, parsley, caperberries, olives and chile; season with pepper and toss to combine.
Add the tuna to the salad and toss gently to flake it. Squeeze the lemon wedges over the salad. Serve with the bread.