so the decision was made (by Churchill, so the story goes) not to warn the population at all.
That urban legend has long since been dispelled, from as early as 1976.
An informative read is RV Jones's Most Secret War: British Scientific Intelligence 1939 - 1945. (Reginald Victor Jones was Britain's Director of Scientific Intelligence during WWII).
In this publication, Jones devotes an entire chapter about the English industrial city of Coventry - which alone of all inland cities of the UK, was levelled during a nighttime bombing raid by German aircraft. The raid on Coventry succeeded simply because, for once, British radio countermeasures failed. In every other case, these measures were successful in neutralising the radio navigation system used by the Luftwaffe's bomber fleet. However, on the night of that raid on Coventry, somebody made a very simple error.
As Jones goes on to conclude on page 150 of Most Secret War:
"It is one of those instances, of which I have since found many, where enormous trouble is taken to get difficult parts right and then a slip up occurs because of lack of attention to a seemingly trivial detail."
Never underestimate the role that a simple, old time £µ€₭ -Up can play in a military disaster!
Straight out arrogance, too, has often played a significant part during failures of intelligence. Pearl Harbor is one example of that. As early as 29th November 1941, the US Secretary of the Navy circulated a general warning that hostilities were imminent. However, Pearl Harbor was not listed as a probable target. Thailand, Borneo and the Kra Isthmus were (correctly) identified as such - but prevailing opinion maintained that Japan was simply incapable of launching an attack on Pearl Harbor. Even after the attack, there were military and naval personnel who were "certain" that those aircraft had been piloted by Europeans.
Three days later, Britain's naval supremacy in the Far East was ended forever by the destruction of "Force Z". This was an event not believed possible - the sinking by aircraft of a battleship flotilla which was under way in the open sea. After these two disasters, both the USA and Great Britain had to come to terms with the fact that they had been bested by a supposedly "inferior" enemy. It is therefore hardly surprising that some wild ideas got circulated, trying to avoid facing up to the fact that they had underestimated their enemy.
Similarly, Israel, too, got taken by surprise in the 1973 Middle East War, simply because it badly underestimated its enemies. Despite all the intelligence reports that came in, which almost screamed out that the Arabs were about to attack, Israel's leadership - both civil and military - refused to believe that the Arab countries were at all capable of doing so. (A series of easy victories during the two previous Middle East wars had lulled them into a dangerously false sense of security).
As was observed afterwards, despite so much information at their disposal, Israel "made the worst possible estimate" of it.
In other words, it is not just a matter of having intelligence data available. Much can then go wrong during the analysis of this information, and wrong conclusions can be drawn when it is coloured by an imagined superiority of the enemy. Also, during the whole process, somebody can slip up during the execution of even a simple detail.
There are plenty of other alternatives to conspiracy when it comes to explaining military disasters. The good old fashioned £µ€₭ -Up has certainly played its role in more than a few!