I am making a TL which is not completely serious, but the US is not sending Lend Lease due to a Huey Long Presidency and the Germans capture Wallied forces at Dunkirk.
Realistically, what kind of peace would the British accept? Would the Germans have the ability to conduct trade with Japan and forcefully emigrate Jews? (See
source.) Would the British categorically not allow the emigration of European Jewry?
The TL is not about any of these things, they allow for an alternate universe where the Nazis become a democracy of sorts and the British essentially become the bastion of global capitalism.
Assuming that Hitler was serious about his willingness to get a quasi-friendship with Britain, it would be a white peace that would have Britain recognize the treaties Germany signed with the continentals, while expelling the governments in exile. Effectively recognize German control of the continent. That would mean no military restrictions, territorial loss, or indemnity except maybe return of some old German colonies. Based on what was being discussed in the British War Cabinet at the time these would have been agreeable terms to them if offered. They seemed to be mostly concerned about any terms that would impede their rearmament, which would include indemnity or military restrictions, though not colonial transfers. Even Churchill seemed open to returning German colonies. Likely if the BEF is lost the Churchill government either falls or Halifax wins the May Cabinet Crisis and forces Churchill to ask for terms in June, which would mean the terms Hitler seemed to be open to, namely no restrictions on Britain, just a recognition of German control over the continent. Likely at that point given that both Halifax and Churchill agreed that those terms would have been acceptable, but were unlikely, had they been offered it would have caught them by surprise and forced Churchill to cut a deal based on his promises to Halifax. So with the deal done the PoWs are exchanged and the war ends.
That's when things get pretty bad for Britain. India upon peace would demand independence, which means it will not be partaking in any renewal of hostilities barring an Axis attack on Britain. Plus at that point India might well fracture along Muslim and Hindu lines and get stuck in a conflict over borders; if not it will have major internal issues to sort out that would probably keep them out of any conflicts in the near future, while the strong pro-German/anti-British undercurrent within Indian politics would make things uncomfortable for the British in post-independence India. The Empire starts to unravel at that point, though slowly, perhaps much more slowly than IOTL without the Japanese attacking in the East. Sure India is gone sooner and would be seriously questionable in loyalty due to the pro-German elements in that society, which would be stoked by Germany beating Britain and their own independence, which might mean strong relations between independent India and Germany, but the rest of the colonies might well hold on for longer than IOTL due to less of a prestige hit to Britain in the long war and far less bad finances with the war ending in 1940. Of course much depends on what happens in the Middle East and with relations with Japan beyond that point, which could end up being pretty bad. Palestine would be a tricky issue going forward...
As to trade post-war yes of course Germany could trade with whomever they wanted once the blockade and hostilities were over. The US and British would lack leverage short of war to get Germany to stop given that the European continent would be under Germany's political control and likely have a German led tariff policy that they could leverage against outsiders and prevent embargoes or at least effectively retaliate if they came up. As to the forcible emigration of Jews...yeah probably. That would probably take on the character of genocide by forcing them in inhuman conditions aboard what would amount to slave ships to go to Madagascar and probably have mortality rates rivaling the Middle Passage of the slave trade. Britain wouldn't really have the ability to stop it short of war. Now I could also see the Germans allowing the smuggling of Jews via neutrals to the Middle East, specifically forcing France into taking Jews to Syria-Lebanon and doing nothing to stem border crossing by Jews into British held territories. Its probably a multi-faceted emigration policy in that case. That also helps set up Britain for a serious problem in Palestine, probably a full on civil war with the Jews and Muslims, while Britain is stuck in the middle fighting a full on war against Jewish refugees. They might well end up being more anti-semitic in the end as a result of what would happen. The Middle East might end up exploding due to the mass arrival of Jewish refugees in the region, plus the Iraqi situation that might take on a different character than a coup ITTL without the war dragging into 1941, while Iran will be a wildcard without British/Soviet invasion in 1941 and Indian Independence in 1941.