The effect of a Nazi victory on the US and England really depends on the circumstances of "victory" and the ramifications. The rule of speculative history is that one can never be sure about what happens, but many alternate historians still try.
In my Nazi Victory TL, the result of the Soviets collapsing and the Nazis winning is a Cold War is between the US and the Nazi Reich. The Nazis massacred one-half of Europe while subjugating the rest.
OTL, the big enemy for many Americans in the latter-half of the 20th century was Communism. This influenced everything: politics, culture, geopolitical strategy, rhetoric by politicians, civil rights, etc. After the Soviet Union failed, that failure became the justification for the neoliberal consensus. The one that says "capitalism must be free in order to be free." The world we live in comes from that geopolitical struggle that lasted from 1946-1991.
TTL, the big enemy is not a dictatorship run by a poorly managed statist model, but a dictatorship with a perverted obsession with racial purity, an open contempt for elected forms of government, a hard-on for conquest, and obsession with mass murder and racial stratification.
TTL, many Americans would see the Nazis as worse than communism. The Nazis, if they brought their nightmarish visions to reality, would not be merely seen as a dictatorship, but an existential threat to human civilization. They've conquered all of Europe, are willing to slaughter millions of millions of people for an autarkic dream, and have nuclear weapons.
How does American racial policy change when a dictatorship that takes American institutional racism up to new heights is the great enemy?
What covert guerilla groups does your secret government agency fund?
What economic policies do you pursue when facing down such an evil regime, and without a communist boogieman?
How does Britain treat its colonies?
What kind of movies and TV are made about Nazis?
In short, there are massive, massive ramifications if the Nazis do conquer of all of Europe.
Clear evidence exists that Winston Churchill was privy to
intelligence reports derived from decoded German transmissions in August 1941, during which he stated:
Whole districts are being exterminated. Scores of thousands – literally scores of thousands – of executions in cold blood are being perpetrated by the German police-troops upon the Russian patriots who defend their native soil. Since the Mongol invasions of Europe in the sixteenth century, there has never been methodical, merciless butchery on such a scale, or approaching such a scale.
— Winston Churchill,
24 August 1941.
During the early years of the war, the Polish government-in-exile published documents and organised meetings to spread word about the fate of the Jews (see Witold Pilecki's Report). In the
summer of 1942, a Jewish labor organisation (the Bund) leader, Leon Feiner
got word to London that 700,000 Polish Jews had already died.
The Daily Telegraph published it on 25 June 1942, and the BBC took the story seriously, though the U.S. State Department doubted it.
Wiki page on
Responsibility for the Holocaust
OTL, however, the US and other governments often looked the other way at these reports. The US didn't bomb Auschwitz when it had the chance, the US balked at welcoming Jewish refugees, and many Allied leaders didn't want to make the war a "Jewish war" in a time when antisemitism was still far less taboo. It was only when US soldiers came across the rotting zombies in the concentration camps that people really took these horrors seriously.
The crimes were so unimaginable, that Raphael Lemkin had to invent genocide to give them meaning.
TTL, I picture it being a few years before anyone would take these reports seriously.
Unless you allow for a let-off valve and let Russians and others run across Urals. We didn’t kill them they moved away can be a decent defense in a time without satellites, internet and with a totalitarian state controlling what is heard and what is not.
Still...information finds a way.