October - December
Operation Sealion launches on October 15. Early results are mixed, although we appear to have surprised the British in the far north as 6th Panzer Group is able to land and establish a beachhead with minimal resistance. However early problems begin to surface: the Fallschirmjager have landed successfully northeast of London, but are unable to break out to the east and link up with 12th Army.
The British are smart enough to concentrate their defensive assets around the deep-water ports, as they appear to have anticipated that we will seek these out. 12th Army cannot make landfall; the marines similarly struggle at Dover and eventually break off the attack; 1st Panzer Group is very late making landfall on the west coast due to weather.

With no relief and no supply, the Fallschirmjager are eventually surrounded and forced to surrender. The Wehrmacht's airborne experiment crashes and burns, as 20 divisions are wiped off the map in one of our worst defeats of the war.
6th Panzer Group's early initial success fades, as it is unable to secure a deep-water port either to the north and south and is withdrawn back across the Channel.
However, all is not lost; 1st Panzer Group is able to make a late arrival in the west and secure a port at Bristol!
December - Welsh Expansion and Reinforcement
By Christmas, 1st Panzer Group is reinforced with two infantry armies and is able to open an expanded front extending just east of the Welsh border. The Wehrmacht is firmly established here, with a firm logistical footing and plenty of deep-water naval capacity feeding in from behind:

The infantry covers the front, threatening Birmingham to the east and Liverpool to the north; von Manstein prepares to strike out with 1st Panzer to the south and cut off Allied forces at Plymouth (in Cornwall).
Three days later, Manstein is on the beaches:

We have extended the front quite a bit here, and would like to wheel northeast with the panzers to flank any defensive lines along the Thames. But we lack the resources to support a simultaneous move east and west, so we hold Manstein on the right flank while the infantry prepares to push westward toward Plymouth.