This was probably the first
political satire TV show back in the very early 1960's on the
BBC. The name was often abbreviated to TW3. It was cancelled in 1963 in the run up to a
general election for fear of affecting the result (a truely more
innocent time).
It was a starting point for a very large number of british comedy careers such as Ned Sherin, Willy Rushton, Roy Kinnear, and Lance Percival.
Some sketches for it are still known today as they are so basic and primal (simliar to the "Parrot Sketch" of Monty Python). Particularly there is a sketch of John Cleese, Ronnie Barker, and Ronnie Corbett which starts "I'm Upper Class ...". This has been repeated and parodied often.
The opening song ("That was the week that was, It's over so let it go ...") was sung every week by Millicent Martin and including lyrics referring to the news of the week just gone. Lance Percival would also sing a topical calypso each week.
It was succeeded in the UK by progams like "Not the Nine O'Clock News", "Drop the Dead Donkey", and "Week Ending".
There was an
American version of it though apparently although it used basically the same format (and the same name and abbreviation) it was not sanctioned and paid no royalties to the UK creators of the format.
One notable point about the US TW3 was that Tom Lehrer did songs for it. Some of these are on his "That was the year that was" album.
Thanks to Gritchka for correcting my facts on Millicent Martin