Ok, so a few things.

1) The Soviet Union didn't want western Europe and had ample opportunity to seize large parts of it regardless of the BoB.

Exhibit A) - Austria. The USSR simply handed Austria over even though they did all the heavy fighting of liberation there against army group South. They could have easily implemented a communist government there, but they did not. They went with Renner instead, whom the allies didn't even recognize anyway.

Exhibit B) Germany. Austria was to the model for Germany but naturally, the allies couldn't keep their promises and decided to divide, rearm, reindustrialize, and reNazify West Germany instead, against all the agreements made at Yalta.

Exhibit C) Greece. How many times was KKE on the precipice of taking over the Greek state, and how many times did the Soviets tell them no, to scale back, to not go forward. The KKE was by far the most powerful party in Greece, with the most powerful army (ELAS), and the only thing that kept them from taking over was Moscow. The KKE was instructed to join a government of national unity and to pursue non-military policies, separating itself from ELAS.

Exhibit D) - The fact that the Soviets had been clamoring for a western invasion of western Europe several years before it ever occurred. But Churchill pursued a peripherel strategy instead, and insisted that oh no, the timing wasn't right, they couldn't do it in 1942, they couldn't do it in 1943, they wouldn't have even done it in 1944 had it not been for American pressure.

2) The Kriegsmarine would have never "driven the RN from the Channel" nor would they would have been able to successfully escort a "flotilla of barges" across the ditch. The Germans couldn't transport enough troops and supplies for the invasion and there were few good landing beaches in southern England. The barges they had were way too few, and too poor in quality. They were in effect using Rhine river barges to cross the ocean that would sink upon any bad weather. They had no ability to transport heavy artillery or armor across. They'd be solely reliant on several infantry divisions, maybe 10. Britain had sufficient forces to mow them down. Furthermore, it is well known that Britain had authorized the use of chemical weapons against the invading Germans had they managed to get across. If the Germans tried an airborne landing it would have been Crete part deux, x 1000.

3) Even if the Germans won the BoB, the British would simply retreat out of range in the north, only to reemerge and fly south upon any attempt at invasion.

4) The Germans had zero intention of invading Britain, knowing full well Sealion was hopeless and having desire to fight the British to begin with. They had always wanted to go east, and had just hoped they could convince Britain to get out of the war.