It is easy to over estimate Alan Turing's contribution to the Allies war effort because for most people his is the most recognisable name associated with breaking the "Enigma Codes"

Because anything to do with Bletchley Park, the war time headquarters and main operating base of Government Code and Cipher School (GC&CS) Britain's signal intelligence centre, remained classified until the 1970s, the small parts that people have heard about become inflated. There were a large number of different codes being attacked there and the work was done by large teams. There were about 10,000 men and women working at Bletchley Park through the war.

Having pointed that out, Alan Turing was one of the important and noted contributors. His work mainly involved breaking the signals that had been encoded using German enigma machines although he also worked on the Tunny code.. There wasn't one "enigma code". A code depended on the settings on the machine, different arms of the German war machine used different settings, and machines of different complexity, and the settings changed daily, so breaking a code meant that you could decipher one day's worth of one type of signal. To decipher signals in time to be useful required large numbers of people and huge amounts of work.

The Enigma machine in different versions had been around since the 1920s. It was designed for commercial and diplomatic use and was adopted by the German military and used throughout the war. I'll address different British approaches to breaking it.

Hugh Foss joined GC&CS in December 1924. He devised a method to solve non-plugboard Enigma in the late 1920s, He was assessing how secure the commercial version of Enigma was for possible use by the British and decided that if you had a “crib” of 180 letters he could work out the wiring settings of the first two rotors and if those were known a crib of 15 letters would, could break the machine settings.. A crib was a plain text portion of the original message. A large part of the codebreakers work, involved guessing “cribs” by looking for standard phrases that might be encrypted in messages, such as addresses, headings for weather reports etc. Possible “cribs” could be tested by being run through a bombe. A successful crib would allow the decipherment of a day’s coded signals using that code. In 1937 Dilly Knox broke the K Model Enigma machine using an improved version of Foss’ system. u/Bag-Weary has discussed the Polish approach using their "bomba". They used a differnt approach than the one used by Knox but the importance of the bomba was that it allowed multiple attacks on a code over a short period of time so that different approaches could be tested quickly. The difficulty in earlier attempts wasn't that the codes couldn't be broken at all, it was that they couldn't be broken in any reasonable time. The British were familiar with the Polish work.

Bletchley Park areas of responsibility were broken down into "Huts". The German Army and Air Force enigma codes were the responsibility of Hut 6 under Gordon Welchman until late 1943. The German Naval enigma codes were the responsibility of Hut 8. Alan Turing was recruited from academe along with other "professor types" in September 1939 and was in charge of Hut 8 until late 1942.

The British "bombes" used a different theoretical approach than the Polish "bomba" leaning heavily on the "crib" system developed by Dilly Knox. Turing provided most of the theoretical design with significant assistance from Welchmann about the probable wiring of the actual enigma machines and the detailed design of the bombe was done by Harold (Doc) Keen, an engineer at the British Tabulating Machine Company.

The Bombe was based on the bomba kryptologiczna (cryptologic bomb) developed by Polish scientists such as Marian Rejewski, designed to crack a simpler version of Enigma than would be seen during the Second World War, with help from French spies with who accessed Enigma cipher keys. This version of Enigma would in fact be cracked before the Second World War even began in Europe, with the Polish operating six such bombi in 1938. The designs were shared with Britain and France five weeks before the outbreak of the German invasion of Poland, when the Polish Cipher Bureau was evacuated from the country, recieving assistance from the French Embassy in Romania and destroying any designs they had left behind.

Not to go too deep into the Enigma's design, but the difficulty of cracking it is proportional to the number of rotating cylinders in the machine. When it was cracked by the Poles, it had three rotors. In 1938, this was upgraded to five, though the German navy had an increased code complexity from the start - first six rotors, then seven, then eight.

It is fair to say that without the development of the Bomba, the team at Bletchley Park would have at the very least been drastically set back in cracking the upgraded version of the Enigma machine. Gordon Welchman, one of Bletchley Park's earliest recruits alongside Turing, said "Hut 6 Ultra would never have gotten off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military version of the commercial Enigma machine, and of the operating procedures that were in use."