It's because the terms in Britain are loaded with cultural meaning rather than just your economic situation (Its part of the reason why the terms don't officially exist now and the systems been replaced with a letter/number system)

I know people who fit in to the exact mold of Middle class (Well educated professional person with a non-physical technical role in an office based environment) who claim they're working class because culturally it fits their identity closer.

Add to that the huge difference within the classes themselves Working class can be your "White Van man with his copy of the sun and a pint of Stella cat calling the women he sees on the street" all the way up to "Very left leaning, educated office workers" and let's not even get into the differences between lower and aspirational middle class