You are thinking in terms of city limits, not the size of the metro area.
"London" city limits were expanded to contain all of its suburbs (and even some un-settled farmland) in 1965, so the present-day city population of ~8 million is substantially the same as its total metro area population. The current London city limits aggregate what used to be 33 county governments, plus countless towns and villages.
NYC hasn't expanded its city limits since 1898! The 1898 city expansion aggregated three county-level governments, and formed new boroughs from parts of two more, to create the current five boroughs. The modern-day NYC metro area population is ~21 million people, ~27 million if you count the distant exurbs, but only 8.5 million live in the 1898 borders.
Chicago's last expansion, excluding the airport, was just a few square miles in 1930. As a result, its current metro area population is about ten million, even though only 2.7 million live in city limits. (Chicago's metropolitan statistical area is unusually small because it is cheek to jowl with other cities, tho)