doesn't mean "frens with Hitler".
At its core, it is the very broad concept of "we're stronger together". More specifically, it is an ideology that sets the protection of [b]the group as its ultimate goal, and seeks to achieve said goal through members of said group working closely together against anyone who'd deter them in it, be it foreign enemy, infiltrator or traitor.
Notice how it doesn't restrict you in how you define the group. It could be a nation, a race, citizenry, employees of some company, members of some club or people sharing the same eye colour. Anything, basically.
Hitler defined his groups as the German nation and the Aryan/Germanic race. (Yes, definitions of race change over time, it is just as much of a social concept as it is genetic.)
Churchill though, he subscribed to things such as "being British", so that probably would've been the group he was thinking of in this context. Notice how this is radically different, and not based on national identity. (I mean, just ask the Irish. Or the Scots. Or the Welsh.) Another possibility is that he meant the Anglo-Saxon. This one would be based on nationality, yet still be a natural enemy to the Pan-Germanic cultural efforts of Germany at the time.
Also worth to note that any group can and do have its own goals regardless of fascism. Fascism itself is not the goal, it is just one of the tools for keeping the group going so that they can achieve the actual goals they might have. It just so happens that the goals of the UK during that time period also opposed the goals of Hitler and Germany.
So there you have it, an eventual conflict was unavoidable. They opposed each other on every possible level. They defined their groups in a different way, their definitions of the groups and the groups themselves were at odds, and their political and material interests also supported identifying each other as enemies.