I just don’t see how it gets you any lasting good as Germany- maybe I am misunderstanding something here.
First you have to succeed, and if you fail, it’s game over. Let’s say you manage to blitz into England an take it. You’ve spent a good chunk of IPCs on a tech that isn’t going to do you too much later in the game. You had to take out fully 6 units on English soil so you’ve almost certainly lost several fighters. Even after you snatch England’s IPCs and get the 8 income from England, this maneuver probably costs Germany 10-20 IPCs (I didn’t crunch numbers).
It also has the opportunity cost that you will make little or no progress against Russia and are virtually guaranteed to be giving up on Africa. With no air support the English Mediterranean Battleship is almost sure to survive, and there is very little hope you will take Anglo-Egypt.
After all of this, you will have at most 1 infantry + 1 tank, or 1 infantry + 1 artillery on the ground holding London. Realistically, you only have one land unit there.
What happens next?
If you took your sub from Sea Zone 8 and took out the Brit’s Canadian transport to reinforce this wild scheme, good for you.
If not: On UK1 the infantry and tank stationed in Canada are up to Sea Zone 2 or 3 and have a good chance of removing your token force. The UK will still have its battleship in Sea Zone 2 or 3 and will get to support this re-invasion with a bombardment. You might not even get to roll a die to defend!
UK1 will also see the UK’s Mediterranean Battleship, likely supported by a Fighter from Anglo-Egypt, smashing up Germany’s southern fleet.
On US1 the US can roll into London with 2 infantry and tank and an artillery. They can support this with the East US bomber, which will land in Greenland. The chance that your piddly remaining troops survive this assault is very low. Just to put the nail in your coffin, the US might have secured Heavy Bombers, Long Range Aircraft (to bring the East US Fighter in as well) or Combined Bombardment (so the Destroyer supporting the Transports can bombard).
So what does this accomplish for Germany? Probably not enough. Essentially what you are doing is forcing a massive, uneven IPC and production trade with the UK. I don’t think the Axis has the economic staying power to sustain this kind of trade. It does buy the German Baltic fleet some breathing room, maybe they could be used in interesting/effective ways.
The UK loses: A full production/income phase while regaining London and a bunch of IPCs and units.
Germany loses: Most of a turn of production, and a bunch of IPCs and units.
Germany also loses: Pretty much any hope of getting traction in Africa. Several fighters that are key to mid-game skirmishes with Russia and later defense/harassment of a rebuilt British navy and American landing force.