In the movie (its about turing decoding the enigma if you didn't watch it), after the Turingmachine worked and they were able to decode the enigma messages, the mathematicians decided not to inform the generals and the King and so on, because they feared that they would spoil it by countering attacks too obvious. So they used statistics in order to inform the generals about some attacks they decoded just enough so that it wasn't too obvious.
I simply cannot believe thats true. I don't think the head of the english army would have been that stupid. They would have concluded that themselves.
No that is essentially just fabrication.
Intelligence from decrypted Enigma messages and eventually all Signal Intelligence or SIGINT gained from the Germans from Bletchley Park was known as Ultra and was used on high levels to keep almost daily tabs on enemy formations and for planning of operations that could take weeks thus by nature not every weakness found would be acted on. But the cryptographers had no say in hat.
Most of the high command and political leadership in both countries was briefed in about Ultra and knew where it was from. Hence why such care was taken to protect them (and why Churchill traveling in a bomber to Tehran was such a possible risk for example). But in the Theater and field commands it was less known and liaison and intelligence officers would be responsible for sharing what was important and what was not.
Just an example to help illustrate but Air Marshall Dowding commander of Fighter Command had a teleprinter link set up right in his command post so that he could receive the latest waning of German formations preparing to attack Britain.
While there was great concern about acting on too much intelligence and tipping their hand it was a decision well above any of the cryptographers paygrades and it was the Generals who were deciding along in most cases. With the closest thing to a gatekeeper being General Menzies (head of MI6) but his role was more to just make sure only cleared people got the decrypts not to decide if they should be sent along.
Alan Turing didn't control what intelligence got pass on, in the end that was Stewart Menzies role. Once the hut 8 broke the naval enigma some moved on to breaking other enigma codes. Turing actually visited the US and started to work on voice encryption.
Alan Turing: The enigma is the biography the movie was loosely based off. It is highly detailed and I recommend it if you are interested in knowing more.
This article goes through the differences between the movie and reality
I watched the movie as well and in the movie they do inform the agent from MI6.
This is where F.W. Winterbotham's book "The Ultra Secret" becomes useful as he ran the distribution system for Ultra (as the decrypted product was known).
Anyway, the mathematicians attacked the messages giving a "menu" to be run on a bombe operated by the Wrens. When they had a match, the settings would be run against further decrypts as many messages may be encrypted under the same key. Broadly this process was run as a production line with messages being sorted as to being either naval or army/airforce (depending on their origin). They would then be forwarded either to Naval Command or to MI6 who organised the secure distribution from HQ down to field through liasion units.
The point being that after the settings were known, the cryptographers were out of the picture as they would be working on the next set of intercepts.
Now Winterbotham specifically mentions the bombing of Coventry as a time when the Ultra decrypts may have been deliberately ignored (not by Bletchley) so as not to reveal that Enigma had been broken but this is considered controversial and many participants at BP stated that although they knew of the raid, they had no idea of the destination.
As for the King, I haven't read anywhere that he knew of the activities of Bletchley Park at the time. He may well have been briefed by Churchill in the one on one weekly meetings held between the sovereign and prime minister but as these are not minuted, we cannot know that. In any case, only a few knew of Bletchley Park's activities, rather the intelligence was attributed to "a highly placed agent" codenamed BONIFACE, and Winterbotham's liaison units ensured that intelligence users were briefed on protecting the source. For example, by the careful positioning of reconnaissance aircraft so it could be deduced that a routine patrol had been lucky to find a convoy rather than attacking it immediately.
If you would like to read about the use of decrypts in practice, I would recommend this piece [PDF Warning] by Vincent P. O’Hara and Enrico Cernuschi on Signal Intelligence and the Battle to Supply Rommel’s Attack toward Suez. In actual fact the interceptions of Rommel's supply convoys were far from complete and many got through. This would tend to reduce suspicion.