How should I treat it? I have previously sprayed it with Natrasoap (Potassium salts of fatty acids), but it didn't seem to have any much effect. Just keep applying it more regularly?
This is mealy bug and quite a well established colony. As this is a plant that you might intend to eat I recommend throwing it out quickly. Some adult mealy bugs can fly when things get too crowded and you do not want them spreading to other plants.
If you apply soap and water or a more serious pesticide the plant will take a long time to recover and not be of any use as a food plant.
Basil plants cost a few dollars and should be easy to replace.