Well, the Germans could have invaded the UK in 1942/43, the problem is(for the Germans anyway) that, of the initial force sent across the channel, only a small fraction would have actually managed to finish the journey.
Let's say about 10 divisions are slated for the invasion and disembark on the continental side of the Channel. Of that, the vast majority(let's say 8-9 divisions of manpower) are killed enroute either as a result of the poorly suited craft, poorly formulated plan, lack of proper cooperation between the different branches of the Wermacht, or direct enemy action. This force will not be a single coherent unit, but rather be comprised of the survivors of the total force, so you're looking at enough men from ten different divisions that have been scrapped together to form one or two whole or partial divisions. This force will have no intact command structure, but rather an ad hoc one set up by whatever officers make it across. It's even possible that they don't have anyone above the rank of captain or even lieutenant as a result of the massive numbers of casualties. This force will in all likelihood have an incredibly lousy composition, so we're looking at a division or two with very few actual front line infantry or armor, but a ton of support and artillery elements or something else equally unsuited for the purpose of securing and breaking out of a beachhead.
So, now you've got a severely understrengthed force arriving on the British channel coast, they are tired, half-drowned, disorganized, their order of battle has been completely shot to hell, and the equipment and supplies that they have access to are probably completely unsuited to whatever forces did manage to make it to shore. Air support will be limited at best as the Germans will never manage to attain anything even resembling air superiority over the British isles. The Luftwaffe and Kreigsmarine will have made huge sacrifices in opening the window for the invasion force to land. A window which will remain open for a week or two at best, and quite possibly less than a day in any realistic scenario, thus leading to this invasion force being almost completely cut off from resupply or reinforcement incredibly quickly. This is of course assuming that the force in question isn't completely overrun well before said window is closed anyway.
Rather than serve to drive the British to the negotiating table, such an invasion would only serve to embolden and strengthen the resolve of the British people as well as strengthen the alliance between the British and Americans as American troops stationed on the British island will undoubtedly be involved in the action in some way. Likewise, it will only serve to further weaken the case of the isolationists in America as a cross-channel invasion will only show that the Germans are interested in far more than just continental Europe.
In the end, such an invasion will actually shorten the war if anything, as the Germans will have just wasted ten perfectly good divisions, and the KM and LW will have been thoroughly mauled by the fanatical response of the Royal Navy and RAF in defending their homeland.
Mind you, this is probably an optimistic scenario from a German standpoint.
As the saying goes, the only winning move is not to play.