This clip was not funny for me, because it was incorrect!
Americans don't seem to be able to distinguish the MASSIVE difference between how educated and non-educated British people speak. In the video that Alex links to, they are only imitating the working class accent, but saying that the person sounds intelligent. They would not sound intelligent to ANY British people! Quite the opposite!
Two people in Britain might grow up 500 metres (a few hundred yards) apart, and speak with completely different accents because they are from different types of backgrounds. One person will sound educated, intelligent and possibly posh. The other will sound like a blue collar worker. It's a very drastic difference.
Apparently Americans, like the host in this show, can't tell the difference!
If anyone is going to speak British English, then the best accent to imitate is that which you hear on BBC, or spoken by people like scientists.
As an example, the character "Daphne" on Frasier, has a Northern working class accent. Yet Americans think she sounds "posh" and typically English. She definitely does NOT sound posh and her accent is typical only of Manchester.