[PzLdr]

I think the Germans would have mined both side of the projected invasion corridor. And there would probably have bee air recon to the west so the germans would have had notice of the heavies [maybe even a U-boat scree]. Plus, your proposed deployment leaves the Germans with heavier guns against the lighter British units [18 X 11":Scharnhorst and Gniesenau, 12 X 11" Admiral Scheer and Luetzow, total 30 X 11"; and secondary armament on the above and heavy cruisers of 5.9" guns, and main armament on German destroyers -superior to all British destroyers, equal, almost to all British light cruisers].

The other problem the British would have faced is that in the Channel, the Germans would have had interior lines, and could re-deploy east to west much faster than the British could get around them.

[Tallguy]

Scharnhorst & Gneisenau were true battlecruisers and would have been formidable. Lutzow & Scheer, while heavily armed, were essentially unarmored and unfit for real naval engagements. Witness what happened to the Graf Spee at the Platte -- she was essentially defeated by a undergunned cruiser force because she couldn't withstand any battle damage. I'll grant you that she was far from home and this factored into her captain's decision to scuttle.

I can't help thinking that if the Germans had attempted the invasion, it would have played out much like the Guadalcanal campaign. Recall that the USMC got ashore only to have the USN & much of their equipment driven off after the Battle of Savo Island. The fighting after Savo was savage. The Marines could only hang onto Henderson Field while the Japanese couldn't really land enough troops to push them off.