@cstross A lot of the fun is in the audio; the visuals are secondary. (If you just don't want to visit the YouTube website, https://inv.nadeko.net/watch?v=QclgVeB6YDo may be an alternative.)
That said, here's my attempt at a written version:
When Americans Write British Characters
[Dramatic background music: Handel's Sarabande in D minor, obnoxiously loud]
Wesley: Rest assured, Hawksworthy, it was my intention to reach out to you sooner, but I confess, I have been in a very bad place of late.
Rupert: [sat in a chair, croaking] Yorkshire?
Wesley: In truth, I often thought of touching base, but with the passing of Lady Chuntly-Brie I needed time to process.
Broadstank: Smoke, milord?
Wesley: I'm good, Broadstank. Can I get a sherry?
Broadstank: I shall fix one momentarily.
Rupert: Look here, old man, let's cut to the chase. Is this about money?
Wesley: How dare you, sir! You know very well I could care less about money. Why, when I inherit, I shall have £10,000 a year, ballpark figure. I believe I shall take a raincheck on that sherry and bid you Good Day!
Rupert: Wesley!
Wesley: Don't you "Wesley" me, Rupert! I simply cannot deal with you right now. Goodbye! leaves
Rupert: Wesley! Wesley! [coughs]
Broadstank: Mr Chuntly-Brie has left us, Your Grace. Shall I prepare milord's mac and cheese?
Rupert: I'm ... dying ... Broadstank ...
Broadstank: Yes, milord.
Rupert: [coughs] Rather funny, isn't it?
Broadstank: No, milord.
Rupert: No, I don't suppose it is. You've always been there for me, Broadstank.
Broadstank: [sheds tear] That's because ... I love you, Master Rupert.
Rupert: I love you too, Broadstank.
Microwave with mac and cheese: [pings]