Hut 8 is where they decrypt naval Enigma transmissions. Hut 4 accepts the decrypts from Hut 8 and analyzes them. If Waterhouse pretends to be a Hut 4 man the disguise will not last for long, because those fellows have to actually know something about the Navy. He perfectly fits the profile of a Hut 8 man, who need not know anything except pure math.