In size, what American city would London compare to?

I don't know about area because compared with the US all British cities are small (but congested). In terms of population, at over 7 million people, Greater London works out a little larger than the urban area of Chicago.

[census.gov/population/www/documentation/twps0027.html#tabB] link no longer exists

As an indication of density, new build homes in the UK are built at between 20 and 50 homes per hectare. London includes many areas of older buildings built at 100 homes per hectare. This is VERY dense compared to most US cities.
Some of the links on http://www.demographia.com/dbx-lon.htm might help. For instance, according to http://www.demographia.com/db-intl-sprawl.htm London is slightly smaller in size than Los Angeles - but note the higher population density. Tokyo is the most densely populated city listed there.