Edit: I suspect the grid squares being used are of different sizes, but even so - the crowded bits of the UK are even more crowded than the overall population density would suggest.
They're about the same size: the UK map blocks are 1 km x 1 km
US: "the United States consists of 11,078,300 Census Blocks." The USA area is 9.834 million km², according to a well-known search engine.
So about .9 km² in average, roughly in line with "Of them, 4,871,270 blocks totaling 4.61 million square kilometers were reported to have no population living inside them".
https://snowbrains.com/map-nobody-lives-usa-47-usa-uninhabit...