Why didn't the Germans detect that their encryption method Enigma had been broken

Not a bad point to make at all and the allies had no field armies engaged until D Day which is seriously late in the overall war.  So the germans were reading all the Naval comms which while helpful, still left a huge gap between INTEL and contact.  Seamen did notice of course, but never decisive as convoy discovery was always inevitable.

Let us be serious here.  all sailings out of halifax were surely collected daily, put in a dispatch in hand on the train to springhill, handed off to an agent with horse and wagon who then went twenty miles down to the beach where a uboat could collect the dispatch.  then sail on out until safe to radio transmit.  They easily knew how many ships are enroute at the start point and could guess potential marshaloing points and do you really think the allies maintained perfect radio silence in the weastern portion of the passage.

for the big events on the Eastern front, there would be ample alternatives for the intel with code leaking just one and not likely even decissive.  a million men attacking at dawn begs the question of their location and just why did we miss them.

important comms were also readily handed off physically anyway by the axis and could be radio commed at a short distance.  most comms were also just not important along thousands of miles of front unless collected and collated and then you watch volume,

They actually did not need to as most intel ages in hours.  

Why didn't the Germans detect that their encryption method Enigma had been broken by the British, given that it was a natural suspect when the enemy seems to anticipate your every move as if he could read your internal messages?

Because there was no enemy “who seems to anticipate your every move”.

The Kriegsmarine was the German navy of WWII. The main signal intelligence agency of the Kriegsmarine was the so called B-Dienst (observation service), which was responsible for attacking Allied naval cryptographical systems.

The B-Dienst started their work already during the interwar years, with their primary target being the British Royal Navy.

The Royal Navy used the following systems at the start of the war:Naval Cypher No1, a 4-figure book used since 1934.

Administrative Code, a 5-figure book used since 1934.

Auxiliary Code No3, a 4-letter book used since 1937 by small units.

The Administrative Code was broken and read by the B-Dienst in 1936, two years after its introduction. Naval Cypher No1 followed in 1938. The Auxiliary Code No 3 was broken in 1939.

Thus, at the beginning of the war, the B-Dienst was able to read all major Royal Navy communications, with the result that the Kriegsmarine was following British naval movements during the Norway campaign in 1940 virtually in real-time.

British security was only strengthened in August 1940 when new codes and cyphers were introduced, but the damage was already done. The systems were fundamentally compromised, and the German codebreakers were only halted temporarily.

The German main effort, however, was now directed against the new Naval Cypher No 3 used in the Atlantic by the British, American and Canadian navies.

Naval Cypher No 3 was created for the Royal Navy, but since no other system had been prepared for inter-allied naval traffic it was shared with the US Navy and the Canadians. The B-Dienst called the cypher ‘Frankfurt’.

The subtractor tables used with Cypher No 3 had 15,000 groups. Since traffic was much heavier than anticipated, code-groups were reused several times, which allowed the German codebreakers through ‘depths’ to reconstruct the tables.

As a consequence, the German codebreakers were able to break into Allied traffic in December 1941. By February 1942, they had reconstructed the code. By December 1942, they were reading up to 80% of intercepted messages consistently 10-20 hours in advance.

From February 1942 to June 1943, the B-Dienst could read the Admiralty U-boat disposition signal that was used to redirect the Allied convoys on a daily basis.

From a German perspective, there was never an enemy who anticipated their moves. Not as long as they were reading the Allied codes plenty themselves.