Overt Nazism was certainly present; not just Rothermere and the Mail, but people like https://en.m.wikipedia.org/wiki/Unity_Mitford and Oswald Moseley.
https://fullfact.org/online/queen-nazi-salute/
Which is one of the reasons Hitler expected Germany and the UK to come to an accommodation. And why he was surprised - even blindsided - when the UK decided to declare war instead.
One debatable defence is that this was still pre-Holocaust, and outright anti-Semitism hadn't yet devolved into mechanised mass murder and enslaved brutalisation.
So it was possible with some moral gymnastics to justify the Nazis as better than the Bolsheviks, who were considered a far more immediate threat to the British ruling class.
Even so. There's no question there was always an undercurrent of support in high places. And in fact the British mythology of Churchillian resistance is at least as much about a nationalist myth of pushback against Germany as a virile and potent competing empire as about fighting the immoral horrors of Nazi fascism and genocide.
The Axis powers started a campaign of world domination and the countries not in the club were not very happy about that. For one, they foresaw being next to be conquered. And no one wants to be reduced to servitude to a much greater power. That is why the war was fought.
I don't think Germany was any more into world domination than Britain and France with their extensive world empires.
Germany lacked secure access to strategic resources and they knew it. Their policies of autarky reinforced this view.
The Nazi leadership also appeared to believe there would be an inevitable conflict between what they saw as Jewish led Bolshevism and the world.
Primary sources are the best for these kinds of questions. “The truth about hitler” (1935) by Churchill provides a good summary of his thinking well before the war broke out.
Everything about Germany at the time was alarming. It’s baffling how no one took it seriously. A militarized dictatorship is a clear threat of another war - which is exactly what happened. Compared to democracies, there is infinitely more danger as an aggressor in conflict. The decision comes down to one man and opposition is silenced.
He also mentions the anti-Semitic views which were already clear in Mein Kampf to everyone. This was not the primary reason of course as peace and security in Europe was always paramount, but if Germany wanted to be anti-Semitic itself all the Jews could leave instead of being hunted down over Europe by a single invading nation and left nowhere to hide which would have left options rather than war.
All in all the idea of “pushback against a competing empire” doesn’t seem to play in my reading of things at all.
https://archive.org/stream/W.S.ChurchillTheTruthAboutHitler1...
There are many things wrong with the UK's view of its own history but the major problem with its understanding of the war is its self image as a plucky underdog. It is absolutely not about a "nationalist myth of pushback against Germany as a virile and potent competing empire". If anything Britain has been at fault for forgetting about its Empire and the moral problems that came with that.