Hitler didn't believe that Britain would turn into an adversary. His idea was for Germany and Britain to rule together - Germany in Europe, Britain in the rest of the world.

It came as a enormous frustration when Britain refused to co-operate.

I'm no military expert or tactician but the ex-British Empire's main core wasn't anywhere else but mainland Britain. If the 'head' was crushed, everything would've collapsed or acquired by the USA. Just imagine: if you were from the colonies & heard that the "mother nation" was f^^ked & conquered, you wouldn't want to contribute at something that was already doomed to fail unless heavy compromises were made. Add forced servitude and you'd have a revolt theatre galore throughout the colonies. After WWI, the 'Empire' was shaking and it was more than obvious. If London and Britain were conquered (the brain & the heart), at least one thing was certain:

-The Axis would've maintain a dominant position in Europe: Central, South, West, North & North-West sides. That would've been a nightmare to fanthom an attack like D-Day. Don't forget that, even if Francisco Franco was reclusive in entering the war, he promised Hitler that Spain would join the Axis only if Britain was conquered & defeated. So, there you go, three four, possibly five, birds with one stone: defeat a major power (or turbid defragmentation at least), establish total control of more than half of Europe, gain another ally (maybe Portugal as well, helping Italy in the process while widening the front), and making Northern Africa, let alone Western Europe, secure.

To an extent, the Eastern Front would be in a foggy prediction in this scenario (and by that I mean it really cannot be known how things would've worked this way) but it would've offered the nazis room to breathe and focus on the long battle. Logistically, the Soviet Union would've had an extraordinary difficult time in being supplied via lend-lease.