These landings would have added another 2 divisions to the German OOB but still wouldn't have made the initial British defending forces 6 Divisions as they would have been met by 50th Infantry Division in Dorset & a Brigade of 4th Infantry Division on the Isle of Wright for a total of 4 1/3 vs 11 German not 6 vs 9.
Well erm no.
First off a division to count as a division must included all of its artillery and support services...the traditional definition of a division being the smallest formation that can operate as an independent force or what lay men might refer to as an 'army'.
The Germans planned to deploy divisional elements...that is not entire divisions...specifically these were the rifle regiments with some attached mountain and/or rocket artillery...the difference between mountain artillery and field artillery is you can break it down into smaller loads making it more easily transportable but the price is you do not get as much bang for your buck. In terms of combat power they were much reduced from divisions, in terms of combat sustainability they were very much reduced compared to a division.
See I am open to the possibility I may be looking at something different after you seem to be looking at XII and XIII corps while my impression is that the German wider front landings would have also brought some of V Corps into the action on the British side. Another problem though is that neither the British defence forces nor the German plan were fixed. We know the precise plan for D-Day because D-Day happened on June 6 1944 providing us a fixed point of time. However any estimation of force deployed by either side in regards Sea Lion is only going to refer to a fixed point of time and we do not know on what day Sea Lion happened because rather awkwardly it well...didn't happen.
A further complication is that the idea of an 'agreed' plan rather ignores that there was no agreed plan...we have records of the Navy and the Luftwaffe reps actually getting up and leaving some of the meetings as the Army was not listening and were just talking among themselves. This also brings up the point that the Army's estimate of what could be carried across the Channel at a given date did not necessarily agree with the Navy's.
Even so for example there were extensive revisions. At one point the 9 division elements of the landing force (not count the airborne troops) was reduced to 7 divisional elements while at one point each divisional element of the landing force was supposed to receive a roughly battalion sized group of 49 panzers this was later reduced due to the problem of actually fitting so many panzers aboard the available landing craft.
Which is not to say that the British were without their own brand of chaos. Units of up to divisional size were formed and broken up, brigades were transferred between divisions, sometimes physically and other times just administratively. Further in counting British forces there is the difference between a Brigade Group and a Brigade to consider. A Brigade in Commonwealth military parlance is equivalent to a German regiment while a Brigade Group includes support units and would indeed function a bit like half a division.
So the options include I could simply be wrong on my 6 divisions in the landing zone count, we could be counting different areas and we could be counting different times after all even just XII and XIII Corps give me 4 Divisions and 1 Brigade (not a Brigade Group) receiving the initial landing by my count.
It may help in deconflicting the division count assessments if one considers that the excellent British rail network could whisk reinforcements in very quickly - without the usual Blitzkrieg disruption of the road network.
Well the transport infrastructure did radically change the nature of the game in the battle of the build up that would have followed any landing. Worse for the Germans the British forces were road transported by motor vehicles and motorised units proved much more difficult to interdict on the march than horse drawn ones. This was in part why the forces the German's deployed in Normandy were so disproportionately (for them) comprised of their panzer and panzer-grenadier divisions...those were the ones that could get there.
Still even holding down the British to German response capabilities (after they had been degraded by months of aerial attack by air forces many times as large) The rather worrying point emerges that the German assault and airborne troops might have faced regular forces equal in numbers to themselves but with much more artillery on day one...let alone the days after.