To make the dressing, combine the mayonnaise, anchovies, garlic, lemon juice, water, cheese, mustard and pepper in a bowl and whisk until smooth. Add the dressing and the lettuce to the shrimp and mix well.
Place a quarter of the shrimp mixture along the centre of a tortilla, leaving a pinch margin at the sides. Fold the bottom of the tortilla up and over the filing, fold in both sides and continue to roll it up tightly. Repeat with the remaining ingredients. Cut the rolls in half before serving.