[Brian Bines]

One of the requirements for invading the U.K. was air control over the Channel to cover a fairly narrow crossing. With most of Eire outside Lufwaffe fighter range air control would have been impossible for the Luftwaffe to achieve. If one looks at the sea distance the various modified barges available to the Wehrmacht for invasion would have to be towed the invasion of Eire looks impossible to initiate or maintain for the logistical reasons and RN superiority as mentioned by Juha. With depletion of the Kriegesmarine ships in Norway and limited Luftwaffe fighter range any such invasion would surely have been a non-starter.
Thats my thoughts on an interesting scenario,

Regards

Brian Bines