RE: “both densely populated cosmopolitan capitals of their respective countries”
She forgot to add the word FINANCIAL before the word “capitals”.
Or she might have been thinking of 1785 to 1790 when NYC briefly served as the capital of the USA.
She used "cosmopolitan" before the word capitals in the sentence, which does the same thing that financial would have, it modifies the meaning of capital in this case. She's not claiming they are the capital cities of each respective country, even though London is, she's claiming they are the "cosmopolitan" capitals. Kinda like Chicago being the murder capital, Hollywood being the movie capital, etc...