If Germany succeeded in occupying Britain, then all of Western Europe is under Axis control. I cannot imagine Spain remaining outside the Axis, and I would expect Portugal to join up for self-preservation. Ireland would probably fall into line in return for gaining the Six Counties. (Sweden and Switzerland would remain neutral and independent, and very cooperative.) Vichy France might even be permitted to join.
So how would "the Allies" come back? That is, the US, the remnants of the Commonwealth and Empire, and the majority of Latin America, including Brazil. We'll assume further that the US crushed Japan in the Pacific, but with the fall of Britain, India declared independence and neutrality, and that the Middle East is controlled by Axis powers or satellites. Also that the USSR was defeated enough that the Axis controls most of European Russia, with a Vichyoid rump state in eastern Russia and Asia. (Don't ask how this came about; ISTM it's a necessary precondition for the OP's question. Also don't ask about nuclear weapons.)
ISTM that the Allies, even with the whole Two-Ocean Navy available, can't successfully invade Europe from North America. The invading force must gain air supremacy in the area, and Axis land-based airpower would be too strong. Also sea control - very difficult near the enemy's bases and far from any of one's own.
I see two possible strategies, which might be carried out in parallel.
One would be "island-hopping" across the sub-Arctic North Atlantic. The massed USN would be strong enough to overwhelm Axis airpower in Iceland and secure the surrounding waters. With Iceland secure, the Allies could take the Faeroe Islands and then the Shetland Islands. From there, an invasion of Scotland is at least somewhat plausible. The Orkneys or Hebrides might come first.
The other strategy would be to invade Africa from Brazil. While Africa is part of the same landmass as Europe, it's very large and communications from Europe are tenuous except by sea - which Allied navies could shut down. The Axis simply lacks the deployable forces to defend the entire coast from Senegal to Angola. And the Allies could move a large force by sea to attack somewhere - say Liberia. IMO the Allies would have much greater ability to project force there by sea than the Axis across the Sahara.- So they occupy all of sub-Saharan West Africa. Then with West Africa as a base, the Allies drive north to Morocco and Algeria. From there, cross into Iberia, then France.
In this case, obviously, the Allies invade Britain from the south.
Two other strategies might be possible.
If there is no Axis garrison in Ireland, a surprise landing there might secure the island before the Axis could redeploy against it, providing a land base for Allied airpower. From there the Allies could invade Britain from the west.
Or... the Allies, victorious in the Pacific and East Asia, could mass forces in China (Manchuria and Xinjiang) and strike at the rump USSR. IMO it would be a weak state, and most of its people, troops, etc., would soon join the Allies. Then the Allies march west to Germany. Britain would be "retaken" after Germany fell (and the Axis surrendered).
