Ten Foot Bunny said:
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Part of that is generational, I think. I stumbled across an episode of Monty Python in late '85 when I was eight years old (thanks, PBS!). The sketch in particular was the guy who was trying to break world records by jumping the English Channel and eating Chichester Cathedral. My mom saw what was on the TV and urged me to watch the whole thing because I'd love it.
She was right, you know! That one episode started my love affair with Monty Python and everything Britcom.

So I grew up watching Blackadder, Fawlty Towers, Mr. Bean (watched every episode the nights they premiered on HBO), Fry and Laurie, AbFab, Vicar of Dibley, Keeping Up Appearances, and Are You Being Served, among many others.
Well, PBS has often been a gold mine. I'm not sure it's so much an issue of generation so much as it is of exposure. A lot of people simply don't watch PBS. Also, my father exposed me to a lot of this stuff, and he was a huge nerd. I notice that British shows and geek culture are like water and sponges. Nickelodeon had some British programming, too. I remember they even ran some movies that weren't released over here at the time. I bet if I could remember any of them, I could find them on DVD now, but back then, I doubt there was the market.
British TV is probably largely responsible for my twisted sense of humour. Though Tom Lehrer certainly helped. And Charles Addams. They just darkened the dry and sardonic approach, though.
Though, I mean, there were also different cultural filters. I remember WEP was given restrictions on adapting anime that prevented death, anything that was culturally Japanese, and Christian symbols. Which is not at all awkward when you consider Voltron/GoLion has a cross on his chest. And, I mean, that happened to a lesser extent in the 90s, with Pokémon having some more minor examples, off the top of my head.
And those can be AWFUL! I still remember the train wreck that was the US attempt at Coupling. The Office was equally abysmal at first when they were simply copying the UK episodes. Almost every funny part of the brilliant original was too much for US censors, and so the US version turned out a neutered, unfunny mess. I was shocked that it lasted beyond the first season. Good thing it did too, because it morphed into a genuinely funny series when they ran out of UK source material.
Dean Koontz once spoke about his books being adapted to film, and the studios basically always wanted to make oooooone change, which usually was some key point of the book. I'm not a Koontz fan, but I sort of think that's a commonality in adaptations of British shows. They seem to want to change the essence of a show in some crucial fashion. I think I encourage them, though. I watch a lot of adaptations--sometimes even back-to-back with the originals--simply because of how horrible they are and how amusing it can be. "Being Human" comes to mind. Not that the original was like,a classic or masterpiece, but it was competent.
I actually sort of wanted the US adaptation of Red Dwarf for, as the kids probably don't say anymore, "the lulz." I'm pretty sure this makes me a bad person.
There are also some that just baffle me. A US version of Luther? Really? I mean, I get that Neil Cross is going to be on board and all, I...I just don't see how anyone thought this would be a good translation.
That's another good one!

I showed my mom a picture of the cast of Trainspotting the other day and she didn't recognize Jonny Lee Miller at all. She also religiously watches Once Upon A Time and didn't recognize Robert Carlyle in the same picture. Strangely, she DID immediately notice Kevin McKidd, and he's the one I think looks the LEAST like he did in Trainspotting. Maybe it's because he's been on US television (Grey's Anatomy) longer than the rest.
My mom weirdly didn't recognise Benedict Cumberbatch as Khan. Or "totally not Khan." That's sort of just a weird tangent, but it came up when my aunt was down and wanted to borrow my copies of Sherlock seasons 1 and 2. That's a REALLY extreme example.