That sounded high, so I checked:

London Density 14,670/sq mi (5,666/km2) (https://en.wikipedia.org/wiki/London)

Denver Density 4,519.94/sq mi (1,745.15/km2) (https://en.wikipedia.org/wiki/Denver)

London has a population density 3.25x that of Denver.

Why exaggerate when the facts are on your side? Or more specifically, why make an explicit numeric claim without confirming that it's correct?

That depends very much on your definition of "London" and "Denver". Your first figure refers to the population density of Greater London, a vast area covering much of what used to be the Home Counties. Your second figure refers solely to Denver City rather than the broader Denver-Aurora-Lakewood metropolitan statistical area, much of which is functionally suburban Denver.

I don't think it's particularly useful to attempt to pin down a fixed definition of the boundaries of either city, particularly one as amorphous as London. Suffice it to say that London is densely populated, Inner London is even more densely populated and rush hour on the tube is genuinely insane; Londoners regularly encounter densities that simply don't occur in most US cities outside of a football stadium and have a subsequent need for far higher throughput than 4G can deliver.

"order of magnitude" is literally the least explicit you can be without just saying "lots bigger". Why be overly pedantic?

I think the problem may be that "order of magnitude more" means different things to different people. Colloquially, it does get used to mean "a lot more", and some people use it because it sounds more scientific. But in a more correct sense, it means "closer to 10x than 1x or 100x": https://en.wikipedia.org/wiki/Order_of_magnitude#Definition.

I personally dislike the phrase and try to avoid it. But if one is going to use it, I think it should be used correctly.

(I agree with jdietrich that the definition of "city" matters)