I remember reading the first book which scooped the enigma story. Title
and author: I forget ;/.

Anyway it said:

1) Britain used decoded E messages to learn what the Germans were
targeting that day during Battle of Britain. Air Command moved their
fighter patrols more or less into the general area where the Huns would
be showing up. This doubled effective air power and turned possible
English defeat into a victory. According to the author, England's radar
system was helpful, but the highly secret E code breaking was what was
decisive.

2) Rommel's Africa Corp went from winning to losing thanks to decoding
messages which had the details of when and where the German fuel
conveys were to show up next in the ports. England let a few convoys
get through in order to hide the fact that they were reading the mail,
otherwise they sank most of the rest, IOW, Montgomery won in Africa
'cause his tanks had a reasonable supply of petrol, and the Huns'
didn't. If Germany's messages were in the clear, they would have had
enough fuel, but they weren't.

3) Germany lost the war in the Atlantic 'cause decoding revealed where
their 'milk cow' tankers were lying in wait to refuel the long range
attack submarines.

4) Decoded E messages told Ike where the German armies were waiting in
France, which changed D day from a giant gamble to an almost guaranteed
success.

Perhaps the book was an exaggeration, but pretty much the author
believed Hitler would have had a stalemate, not a defeat. Except for
the captured Enigma devices which enormously aided the economical
deploying of Allied forces.