London has a ridiculously large amount of people in it considering its size and archaic design, yeah, but the 'vast swathes' of English countryside are almost non-existent compared to the real major countrysides of the world in places like Russia or even the US.
To compare, the US has a land area of 9167 thousand square kilometres. The UK has 242. With forty times the surface area, the US only has five times the population. The UK is pretty full, really.
But that said I just looked it up and it seems the UK only comes 28th on the population density list. Humm... and Japan is only 20th... Heck! Belgium is 19th!