The posters are all correct: London (not London's something) must follow the modifier "having been bombed..."
It seems to me that this question intends to test two concepts: (1) the idiom "took on" and (2) the choice of a subject noun (or nouns) that could logically take on "... mythic significance." The existing explanation for (A) alludes to the misplaced modifier, the same explanation we should find for all the other choices! Also, I think the real GMAT might take issue with "it" in the original sentence. I think the antecedent of "it" is reasonably clearly "the Blitz," but I find "after it" to refer to an event a bit unidiomatic. You could leave "it" in, as it provides yet another reason the original is not best, but here's what I'd propose to fix this question:
Though the city had been bombed for fifty-seven nights in a row,
the Blitz and the refusal to surrender London afterward took on almost mythic significance as evidence of British citizens’ ability to resist the will of Hitler and Nazi Germany.
(A) the Blitz and the refusal to surrender London afterward took on
(B) London’s Blitz and the refusal to surrender took after
(C) the Blitz and the refusal of the city of London took over
(D) London’s refusal to surrender after the Blitz took on
(E) London’s refusal to surrender after the Blitz took up
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Emily Sledge | Manhattan GMAT Instructor | St. Louis
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