Break the tuna with a fork and transfer to a blender together with the egg whites, cheese, anchovies and lemon zest. Blend well, pour into a bowl, add the potatoes, olives, capers and season with pepper.
Wet and squeeze a sheet of oven paper and spread on a work surface. Place the tuna mixture on one end and give it an oblong shape with your hands. Roll the paper over it and secure both ends with a string. Drop into a pan of boiling water, then simmer for 45 minutes. Lift it out, cool and leave in the fridge for at least 2 hours (preferably overnight}. Blend the basil leaves, oil, lemon juice and salt, and serve with the sliced tuna loaf.