George Orwell ends his essay The Road to Wigan Pier (1937) with (emphasis mine):
And then perhaps this misery of class-prejudice will fade away, and we of the sinking middle class … may sink without further struggles into the working class where we belong, and probably when we get there it will not be so dreadful as we feared, for, after all, we have nothing to lose but our aitches.
Earlier in the same book, he comments that (again emphasis mine) In almost any revolt the leaders would tend to be people who could pronounce their aitches.
I am missing some context to understand this; probably both due to me not being a native speaker, and due to the comment relating to a situation 80 years ago. In both cases, Orwell is discussing class distinctions and class prejudice, so pronouncing the aitches is presumably a pars pro toto for a larger sociolect belonging to a particular class (and to non-linguistic class distinctions as well). But he chose to describe it by aitches, so that must be or have been a major characteristic.
How did the pronunciation of the h within England in the 1930s depend on class, and is still still true today?
Edit: (I am aware that this is a reference to Marx' they have nothing to lose but their chains , but my question is rather about the sociolect he is referring to than about the historical or political context)