It ran from 1981 to 1982.
https://m.youtube.com/watch?v=kAoo349MFCM

Peter Cook was one of Britain’s top comics. He worked with Dudley Moore from the early 1960s to the late 1970s, but unlike Moore, Cook never became famous in the US.

I wonder why Cook decided to take the role. It was far from his edgiest work. FWIW, I think Cook’s humor was too raunchy and mean.

A precursor to Who’s the Boss. I thought it had potential and should have lasted longer than two seasons. Plus, I’ve always loved Mimi Kennedy (who’s now on Mom, and was so fantastic on the late, lamented Homefront).

Simply terrible the way he and Moore made me laugh so hard, specialty..especially..if frogs & peaches came up.

Like many comedians, Peter Cook had a self-destructive streak that took him much too soon.

When Bad '80s Sitcoms Happen To Good British Comics (http://zvbxrpl.blogspot.com/2008/03/when-bad-80s-sitcoms-happen-to-good.html)

In the last couple of days I've re-discovered not one, but two short-lived U.S. sitcoms starring great British comedians who were hoping to pull a Dudley Moore. (That is, become a big success by doing their British thing in an American setting.) The first is "The Two of Us" (https://web.archive.org/web/20061031132420/http://www.jumptheshark.com/t/twoofus.htm) (1981), a remake of the British show "Two's Company." (https://en.wikipedia.org/wiki/Two%27s_Company_(British_TV_series)) The original starred Elaine Stritch as an American living in England who clashes with her snobby British butler; the U.S. version had the same situation except the show took place in America, the woman was played by Mimi Kennedy and the butler was played by Peter Cook. This was just after Dudley Moore had become a big star in America and it seemed logical for Cook to try his luck there, especially in a pre-tested property, but based on what I've seen of it, the show just wasn't very funny. Not terrible, just not very well written and without taking full advantage of Cook's amazing talent.

The other one is "Nearly Departed" (1989), starring Eric Idle, which I actually watched at the time on NBC. I strongly suspect that I was its only viewer, since it only lasted four episodes. (Some additional unaired episodes were shown in England.) It was like Topper but probably directly inspired by the success of Beetlejuice with Idle and all-purpose floating sitcom player Caroline McWilliams as a couple of ghosts who live in a house with an annoying sitcom family that includes the always entertainingly daffy Wendy Schaal (whose father, Richard, appears in the "Two of Us" clip above). The only person in the family who can see the ghosts is the grandpa, once again re-enforcing the message all Hollywood executives believe: old people might as well be dead anyway so why shouldn't they be able to communicate with ghosts? The director of the show was the great John Rich.

As I recall, the show was a bit funnier than "The Two of Us," (https://en.wikipedia.org/wiki/The_Two_of_Us_(1981_TV_series)) mostly because Idle was sometimes allowed to break out of the format and do his thing. I remember in one episode, for absolutely no reason whatsoever, he did a monologue for a full minute in the voice of his ex-employer David Frost. (You'll remember that Idle did his Frost impression a number of times on Monty Python including the classic Frost-bashing sketch "The Timmy Williams Show.") There was no excuse given for this; he just said: "Hi, everyone, I'm David Frost," and started doing the voice. Very dopey show, but at least you got the feeling that it was just a dopey show rather than the sinking feeling I got with "The Two of Us" (http://www.imdb.com/title/tt0081953/) that this part could have been played by anybody. (Of course, unlike Peter Cook, Idle then went on to do a whole bunch of other stuff in America, including some things that were even worse than "Nearly Departed," like the final season of "Suddenly Susan.")

And one more thing, if you've gotten this far: a promo for "The Two of Us" actually uses the term "With hilarious consequences." And here I always kind of thought it was a made-up cliché that no TV announcer had actually used.

I remember it! Can't say what my impression of the show would be today, but at the age of nine, I enjoyed it.