Obviously NYC is denser etc. So it's a very rough sketch, not an exact one and not to be taken too literally.
I'd say Central London is the "Manhattan" with a bit of Brooklyn thrown in. The East End itself can be a sort of Lower East Side/Williamsburg hybrid.
NW London = Queens (most multicultural, largely interwar suburbia) with a bit of Brooklyn.
NE London = Bronx (most deprived cluster of boroughs, lots of housing projects).
South London is harder. SE London is the the whitest borough and mostly working and lower middle class and the least densely populated. It's Staten Island but with old-stock Brits instead of Italian Americans.
SW London = no clue. Mostly middle to upper middle class. Not very diverse, but more so than SE London.