In the movie "The Imitation Game," it showed Alan Turing and the Bletchley Park Hut 8 team cracking what is probably the first enigma message cracked by the British: heading commands for the German torpedo boat KMS Jaguar.
I'd just like to see if any other historical texts or entries either verify or go against this story. As far as I have researched, no historian has recorded the first Enigma code cracked by the British. In addition, the Poles were the first to crack Enigma before the British, correct? What was their first message that time? Similar to my research with the British codebreaking scene, no historian has documented the first code broken by the Poles.
Of course, with them only declassifying the Enigma-cracking strategies after the war (and the Poles declassifying their strategy before the Battle of Britain), it might be hard to deduce what the first message could've been, but I would still like to know if it has been documented anywhere, or will we never know.
This is a tricky question to answer, because there wasn't really one Enigma cipher. Enigma was really a family of related cipher machines, used by the German military and state. Different services had different machines and different procedures for using it, which could make decrypting their messages easier or more difficult. These also changed over time. As such, different approaches had to be taken by the Allies and what we can consider the first decrypts changes. That said, you've given a scenario that does constrain what we can consider our first decrypt - the first messages seen by Alan Turing and Hut 8.
Hut 8 was the main part of the Bletchley Park organisation responsible for breaking the German Navy's Enigma. The Naval Enigma was more complex than the systems used by the German Army or Air Force. These two services issued their Enigma operators with five code wheels, with the operators using three to encipher messages. The Navy's Enigma had a choice of eight wheels. The Navy also used a more complex procedure for transmitting the message settings (which I've described here), making it harder to break into intercepted messages. This new method had been introduced in 1937, and while the Poles had been able to break some earlier Naval Enigma messages, they largely were not able to continue this success under the new system. The exceptions came where one ship, a torpedo boat referred to only by its callsign AFA, obtained permission to use the old system until it could be issued the tables required for the new system. The Poles transferred a lot of their work to Britain, and Turing's work on the Naval Enigma built off it.
Turing started working on the Naval Enigma project in the latter half of 1939. Despite some helpful information gathered from prisoner interrogations, this work was initially somewhat futile. He could not find a way into contemporary traffic without the vital supplementary material of the bigraph table. Some early messages from November 1938 were broken in the winter of 1939-40, but these could have little impact on the war, being a year out of date. Unfortunately, I can't find any listing of these early messages. In April 1940, though, the luck of Hut 8 changed.
On the 26th April, the British destroyer Griffin encountered a suspicious trawler, claiming to be the Dutch ship Polares. Griffin's captain sent across a boarding party - a decision that paid off, as Polares was actually the German armed trawler Schiff 26. Schiff 26 carried an Enigma machine, but the British boarders were not able to capture it. What they did secure was a hoard of significant extra material:
With all of these, the British were able to make a fairly rapid decryption of a number of day's messages, with the work mostly being done by Joan Clarke. The 23rd and 24th fell easily, and the 22nd and 25th which used some of the same initial settings, soon afterwards. The 26th, where the British did not know the initial settings, took two weeks of bombe time to break. This also proved to give the settings for the 27th. Breaking more days was a considerably harder challenge - May 8th 1940's codes wouldn't be broken until November of that year.
The decrypts from the first of these days to be broken (23rd April 1940) have not come down to us directly. What we do have is a British report listing the contents of these decrypts. They largely relate to the movement of ships and personnel along the coast of Norway. While the report doesn't list the precise order in which the signals were decrypted by the British, I'll reproduce in full the first chronologically (capitalisation as in the source):
ADM. WESTKUESTE informed GRUPPE WEST and ADM. NORWEGEN that there were no salvage tugs available at HAUKESUND or STAVANGER. He requested that two powerful salvage tugs should be sent to Bergen.
Other messages include a question from a senior officer about ships in Bergen and Stavanger harbours, two messages about submarine warnings, and permission for the harbour commander at Narvik to go on leave.
As I've noted, these weren't the first Enigma messages to be broken. Nor were they the first Naval Enigma messages to be decrypted. What they were were the first wartime Naval decrypts.