Orwell, a brilliant writer, used "the sheer vulgar fatness of wealth" as metonymy to represent an aspect of wealth that was very unattractive and indulgent during a period of time before 1914. The time period that he referenced was the one before the start of WWI which, I am convinced, has significance therein. In context, he mentions that the absence of aristocratic elegance, meaning the absence of the elements of refined behavior associated with nobility, was so "obtrusive" (intrusive in an unwelcomed way) and prevalent during those aforementioned years. Orwell's intent was to highlight an ugly aspect of overindulgent wealth. Historically, "fatness" or "obesity" has often been used as a biased description for extreme wealth. Caricaturas have depicted this bias of $$$.

"The sheer vulgar fatness of wealth" Meaning the absolute or the total of wealth, which is vulgar, meaning disgusting or offensive