We know the method, but we also need the key used for any particular message, unless Enigma has been thoroughly broken. IIRC (from The Code Book), at the end of the war Bletchley park couldn't break German naval messages. (They used the same machine as everyone else, but with less predictable messages.)
The search space is small enough that the only "hard" part is telling if the message is properly decoded. They might not have used predictable messages but simply testing for the number of German words / phrases in a given output should work just as well. Assuming the actual messages are not overly cryptic.
In short, the Navy, specifically U boats, used a non-standard, stronger crypto (in this, more rotors) Enigma machine, called M4. They formed their own Enigma network called "Triton" which the allies called "Shark".
Due to their hardening, and less message sent for traffic analysis, these machines were "safer" against cryptanalysis.
Wasn't the whole point of Collossus that it was brute-forcing the messages on the more complex Naval keys until it found a candidate match? That's certainly what I remember from visiting Bletchley Park.
In any case, there are now (finally!) software implementations that are significantly faster than the reproduced hardware Collossus, so even if I'm not fully right brute-forcing messages should be viable.
Tunny was the British codename for data from the Lorenz machine, which is what Collossus was working on. The original Enigma machines were attacked by Bombe machines developed by Polish codebreakers pre-war.
Am I missing something?