If you assume unconditional surrender following a massive invasion then it’s anybody’s guess. I reckon a negotiated peace in 1940, with no invasion of most of the UK was perhaps more likely.
Enough of the British upper class were sympathetic enough to the anti-Bolshevik/anti-semitic/social discipline agenda that forming a respectable British government willing to make peace with Germany would have been perfectly feasible. If the army had been entirely lost in France or at Dunkirk and the airforce had collapsed in summer 1940, a negotiated peace, without full occupation, would have been perfectly feasible. I’d hazard that people would have been quite relieved not to have their cities flattened. The king would have talked about the proud people of Britain and germany having much in common. Stability would have reigned. Industry would have prospered. There would have been a customs union and that sort of thing. Hitler is pleased to have the irritant of Britain out of the war, and even more relieved not to have Britain soliciting US aid. He is well aware of the vast US contribution to finishing germany off in 1918, and avoidance of the US weighing in is the single biggest achievement of the peace treaty with Britain.
Britain as a land-mass would have been of modest strategic significance, I’m sceptical that a major occupation would have been necessary. With Britain out of the fighting, Ireland might well have come off the fence and allowed submarine and air bases on their Atlantic coast, so apart from perhaps wanting submarine bases up in Northern Scotland it’s hard to see why Germany would press for many bases or garrisons.
The main significance is that British control of Suez and the middle east ceases to be an issue. German shipping can suddenly pass through the canal unimpeded, and its sea-lanes in the Pacific are protected by the British navy. German ships have free passage along the African coast and the huge markets that opens up.
The British navy supports German troops fightig through Greece towards the Bosphorous, and allows German control of Iraq. Germany now has access to vast oilfields and is able to push into the USSR from the south across the Caucasus. The British navy pushes up the Baltic and harrasses Russian supply lines. Without Churchill’s mediation with the US, Roosevelt does not send military supplies to the Russians. Russia collapses in 1944. Germany can consolidate, with unimpeded Western sea-lanes, access to middle eastern oilfields and varying control over most countries of Western Europe.
With no enemies to the North, German occupation of N. France or the low countries is not necessary. These countries have german attached military advisors in most units and staff headquarters. France, Ireland and the UK join Spain as politically compatible countries in a military alliance under german leadership. Their political cultures move towards Nazi ones (much admired in many circles in the 1930s) but with victory over the Communist menace assured and their economies powering ahead, Western European leaders do not find the need to scape-goat their jewish minorities particularly. The worst excesses of the holocaust are not felt in Western Europe, although the yiddish-speaking population of eastern europe is virtually wiped out as German lilitary controla nd the long war against the USSR grinds East.
It doesn’t seem very important at the time, but the zionist settlements in German-controlled Palestine are largely wiped out. Hitler gives the go-ahead to Haj-Amin to organise the complete destruction of Jewish religious sites in Jerusalem. Skilful political manipulation of Arab leaders produces Ba’athist governments in Iraq and Syria. German military control of the Suez canal is complete, but it prefers to leave local security and control of the oilfields to corrupt and unrepresentative oligarchies with whom they can deal.
We could keep this up for ages, couldn’t we? Going to stop.
