It's funny how people who live in the UK (tho this is Irish) mock Americans for thinking they all have the same accent yet topics like this do the same thinking the yanks all have the same accent. Brooklyn (pre hipster) sounded different than most NYC people. NYC in general sounds different than Boston. Georgia Southern accent is vastly different than a Tennessee accent. Where I live we don't have an accent at all. There is no singular 'American Accent' at all.
To be fair the amount of accents in the UK is quite uncanny for such a small area of land in comparison to the US. It's honestly something I look to be just a signature and one of the most famous stables of British culture.
From what I've found online is that there are about 56 main "accent types" in the British Isles, but within each of those accent types there are scores or even hundreds of distinctive variations. In comparison there are about 42 recognised accents in the USA with much less town-to-town variation and much more mutual comprehensibility.
I personally have never mocked a group of people for sounding all the same (to be honest I don't get what there is to even mock in that), although every country has a stereotypical accent whether it be American, English, Scottish, Canadian, French or Irish so on and so on that people just associate with each country.