The Axis powers were revisionist powers intent on upturning the international order as it then stood so they could expand. Britain was the premier example of the power who benefited from that international order since it had essentially created it. As a status quo power, it has nothing in common with the Axis. Their gains have to come against British power and influence.
Even in a best case scenario where Hitler genuinely wants a British power that retains its empire and is friendly to Germany, Britain likely suffers some severe losses. 1) Canada defects to the American orbit, either out of fear of fascism or under American pressure. 2) Likelihood Australia and New Zealand does the same as it seeks someone to protect them from Japan. 3) Britain is chased out of East Asia by various (perhaps with face saving) means as Japan consolidates it hold. 4) Britain returns Germany's African colonies to it. 5) South Africa under Boer domination effectively removes itself from the British Empire to accommodate the new German one.
Economically, Britain becomes a big loser as the kind of international trading system Hitler uses undermines British trade ties. Eventually the German economy dominates it, and British prestige, power, and influence declines as it becomes the junior partner to Germany.