In my view, there are just two "classes" of people - those that need to work or to receive benefits in order to live, and those who can live off the the interest and dividends that their wealth provides for them.
There have been so many different definitions of what class is and, I believe, an unhelpful preoccupation with who belongs to which class. At one time I seem to recall it was determined primarily by the sort of job that a person did, save for the "upper class" which was split into two levels upper upper - aristocrats/landed gentry/ "old money" and lower upper - business owners/entrepreneurs/"new money". Different class structure models put different emphases on various other factors, such as education/parents' education, "lifestyle", blue collar/white collar/professional occupation, etc. etc. To my mind, it is all a nonsense.
I can see no point in having a class model, other than to make the majority of people believe they are superior/more deserving than one group and/or inferior/less deserving than another (as the TW3 Corbett, Barker and Cleese sketch demonstrated so well).