London in 1930 is the height of the Great Depression for Londoners. I think by 1933/4 we were slowly climbing out of it. However this is the Age of Austerity after the glitz and glamour of the 1920s. Of course the glitz and glamour only applied to certain classes but everyone in London, via lots of magazines etc, would have been aware of the Roaring Twenties. Lots of people have drawn parallels between the 20s/ 30s to the first half of the 2000s and the last few years.
London at the time would have a huge poor/ rich divide, with high levels of unemployment amongst the poor. The rich would have lost a lot of money as well ( I think Churchill lost a lot of his fortune in the Wall St. Crash) but because they have a lot anyway it doesn't matter.
Also class- since WW1 class boundaries have been slowly breaking down and therefore class boundaries are less strict BUT still firmly in place, and everyone would be well aware of it. One class that's particularly changing is the middle-class, as they throughout the 19th century could afford large houses and servants, but this is no longer possible and so increasingly the middle-classes begin to cook/ do housework for themselves.
Also homosexuality is still illegal, women are treated worse than men (having only had the vote on equal terms with men since 1928) and racism is very, very widespread. Also no birth control (legally- back street abortions were available) so, unless the mother was unable to/ father's dead or their relationship is platonic I think there'd be some siblings.
And there's a good chance the girls parents would have witnessed WWI. The father might have fought in WW1 unless he was skilled in a particular job/ couldn't for health reasons/ was a Conscientious Objector. At least they would know a few people who died in the war and the mother might have helped as nurses or in war work of some sort.
Is there a specific area of London you want to set your story? If so there are some very helpful local history websites of most London boroughs so you can do some research there.