It's recognizable and easy enough to fake, at least to the degree that another American would recognize it as British English. Most people would not recognize a (say) New Zealand or South African accent, much less be able to replicate it.
It's also interesting that it's always a "posh" British accent: nobody ever fakes Cockney or Scouse or something.
> nobody ever fakes Cockney or Scouse or something
The article specifically refers to faking an "Essex" accent. The Essex accent they're referring to is basically a cockney accent, softened a bit. When East London was gentrified, from roughly the 70s, many East Londoners moved out into Essex.
It's also interesting that it's always a "posh" British accent: nobody ever fakes Cockney or Scouse or something.