I spent the better part of my teenage years eating raw carrots to be a better Ninja!
I don't know if they ever thought the myth would catch on as well as it did, but it's still widely believed today. (Perhaps because there's no downside, eating carrots is still good for you, it just doesn't improve your eyesight.)
> whilst the [British] Air Ministry were happy to go along with the story [of carrot-improved vision], they never set out to use it to fool the Germans.
> The German intelligence service were well aware of our ground-based radar installation and would not be surprised by the existence of radar in aircraft. In fact, the RAF were able to confirm the existence of German airborne radar simply by fitting commercial radios into a bomber and flying over France listening to the various radio frequencies!
Link: https://www.scientificamerican.com/article/fact-or-fiction-c...
I wasn't however able to find if there is any reason for the british to push such a message if it wasn't to confuse the germans.
Carrot cake also had a surge in popularity at the time (if the great show "Supersizers eat..." is to believed).
Could it have had something to do with rationing? Perhaps they were trying to increase carrot consumption.
It can also be that they wanted citizens to cultivate more of it in their home gardens for its nutritional values. But either way, I have no data to confirm it.