Mammalian Musings...
The only reasonably coherent book I've ever read on a possible successful German invasion of Britain was by Kenneth Macksey and published in 1980 I believe. Basically, the invasion occurs in mid-July with the Battle of Britain in late June-early July.
There are plenty of holes but it's worth a look.
I prefer to think about a possible negotiated settlement between Britain and Germany and the ramifications but this has been done to death in various scenarios both on this forum and in other books.
Essentially, there are three possible outcomes:
1) Fortress Britain: - the country remains neutral and unoccupied while Germany and the USSR slug it out. Defences are built up so as to make any invasion attempt almost impossible. IF the Germans prevail in the east, they will be too busy there to worry about the UK. IF the Russians prevail, the Red Army sweeps across continental Europe and a new threat stands across the Channel.
2) The Fatherland Option - a successful Germany negotiates a peace with the USA once the latter has defeated Japan. It becomes increasingly difficult for an isolated Britain to remain apart so at some point in the 1950s Britain joins the new Germania.
3) The Nuclear Option - events occur as in OTL and after Pearl Harbour, the US and Germany go to war. Britain abrogates the treaty with Berlin and resumes hostilities in 1942 and comes under suatained air attack. In the end, the first atom bomb is dropped on Hanover with a second on Munich and the Nazi regime collapses. In the confusion that follows, the Continent is partitioned between Washington and Moscow.
There are other possibilities of course.