Regarding this thread's scenario, while the blitz focused on the East End, the V1s would hit all over London. So Whitehall, the West End and other parts of London would be hit hard too. That's why I'm suggesting the ruling class might not be quite as stoic.
I would suggest going to things like Mass Observations, where period attitudes and thoughts are recorded.
ATS 230873, for example, was trained in London, and shifted loads by truck around London - including trips to the East End during a period that included V1 attacks. (My Uncle Patrick claims to have had a lengthy conversation with said subaltern, with varying degrees of detail given depending on the audience. However, Uncle Patrick was not an honest man, and examination of his war record shows that at the time in question, he was in Burma and not, as he liked to pretend, up to black market shenanigans in London).
Early in the war, there are the well-known examples of night clubs continuing to be patronised during air raids.
By and large, those of a non-stoic nature had departed London early on, on one excuse or another. Those that remained were the bloody-minded sods.
I would strongly, strongly, strongly suggest reading the diaries and memoirs of the people of the period, rather than trying to guess at their attitudes.