Not at all.
Firstly - getting into a discussion about social class is doomed to failure - no-one can agree, and it's so, so subtle and nuanced that it's almost impossible to talk intelligently about.
Secondly - I know lots of poorly-paid academics who live in tiny flats and houses crammed with books and nice objects and pictures which express education, sophistication and cultural awareness. That's solid-state middle-class in my book.
Also - lots of people in 6 bed houses with about 30 bathrooms who don't know their arse from their elbow in terms of culture. I don't think they're middle class. They're rich, and that's different.