So true! Sometimes I'll watch a repeat of YM/YPM and find myself shaking my head in bewilderment at how it parodies something that has been in the news that very day, even almost down to exact phrases and quotations - amazing considering it was written 25-30 years ago. Brilliant lead and supporting cast as well.
There was a forerunner to HIGNFY in the late 60's called Quiz of the week. Hosted by Ned Sherrin and team members of Richard Ingrams, Willie Rushton, John Wells, Peter Cook Etc.
A TV version of Private Eye really.
At the moment, even though MtW and HIGNFY haven't been as consistently good in the last few series I still watch them, but The Thick Of It is probably the show that is still at the top of it's game.
Not sure if these count but i'll put in a shout for them anyway
Newswipe / Screen wipe
The News Quiz
MtW is not fit to be mentioned in the same breath as the others you have listed. It's not topical satire. It's a bunch of smug soRAB failing to be funny.