Yes, a number of Allied codes were broken during the war. In particular, the Germans and Italians found considerable success in breaking British naval and diplomatic code. These were generally simpler than Enigma or the Japanese 'Purple' ciphers. Instead of using a machine to encipher the message, a book was used. This book contained a list of words, with each word having a corresponding number that represented that word in the code. There was also a system for spelling out words that weren't contained in the glossary. Book codes like these were simple to produce and use, but were less secure than a cipher machine.

The German and Italian navies both had organisations to break the codes used by their Allied counterparts. The German organisation was the 'B-Dienst', formed following WWI. The Italian Navy's codebreaking organisation was part of the Reparto Informazioni dello Stato Maggiore della Marina, the naval intelligence service. It was led by two officers, Giorgio Verità Poeta and Luigi Donini, and formed in 1931. These services combined intercepted naval signals and intelligence from agents abroad and at home to work on the British codes. They were aided in this by careless British practices.

These two organisations quickly broke the main British codes. The Italians broke the Administrative Code, used for communications with merchant ships, in November 1934; the code had only been introduced earlier in the year. The next year, the B-Dienst would see similar success against it. The Naval Cipher, used for communications between merchant ships, was harder to break. The Germans were only able to break it in 1938. In the same year, an Italian officer bribed a signals NCO aboard the destroyer Decoy, giving the Italians a copy of one of the two code books used for it. The Italians were also able to obtain copies of British diplomatic codes through lax security at the British Embassy in Rome. As Germany and Italy drew closer, information was shared between the two organisations, compounding the effects. By the start of the war, both the Germans and Italians were largely able to read British naval communications within the day of interception, and to track British deployments well.

These successes continued after the start of the war. While the British introduced new code variants in August 1940 and January 1941, the Germans and Italians were able to break them fairly swiftly; Naval Cipher No. 3 was broken within a year of its 1941 introduction. This access to British messages led to a considerable number of successes. In July 1940, the Italians deciphered a message which showed that the British had been able to break one of their tactical ciphers, SM 19S. This led to the establishment of new security procedures, which meant that the British were unable to read the codes used by the Italian Fleet. They also managed to plan a number of ambushes of British light forces based on intercepted messages. B-Dienst saw considerable success in helping the German fleet avoid interception in the run-up to the invasion of Norway in April 1940, and helped U-boats and surface raiders intercept convoys.

However, unlike the Allies, the Germans were careless with the information they gleaned from codebreaking. U-boats made deployments that were so perfect they could only have been made using information taken from Allied messages. B-Dienst made no attempt to disguise the sources of information in radio communications. This meant that, in May 1943, when both the Allies and Germans were able to read each other's messages, the Allies were able to determine that the Germans had broken Naval Cipher No 3. Similarly, in November 1943, the Allies discovered that the Germans had broken its replacement, Naval Cipher No 5. As a result, they switched to more secure machine ciphers.