Around the time that Woolf was writing Mrs. Dalloway, social standing was very important. Society was concerned with appearances and maintaining their image. This is apparent in Clarissa's concern with throwing her party. While those who were well off were able to entertain themselves with hosting guests and preparing for events, there was a clear divide between the upper class and the lower class. While Clarissa and those in her circle are simply trying to maintain their social standing or improve it, others around them such as Miss Kilman despise them for it.
The effects of the war differed between class, "Poverty amongst the unemployed contrasted strikingly with the affluence of the middle and upper classes." [1] This leads to a clear divide between the lower class and upper class, creating tension among characters like Clarissa and Miss Kilman.
The climate surrounding social class at the time was one where the well off became even more well off while those who were impoverished were even more disadvantaged with unemployment rates increasing. These societal factors present themselves within the text when considering the relationship between characters such as Clarissa and Miss Kilman & Ellie Henderson. Ellie Henderson's presence is a clear example of the class gap present in their society. Clarissa's reluctance to invite her and her refusal to talk to her at her party is because of the difference in social standing.
[1] https://www.historic-uk.com/HistoryUK/HistoryofBritain/The-1920s-in-Britain/