So, I watched the No News clip and went exploring. I found this:

Time Trumpet was a six-episode television comedy series which aired on BBC Two during Summer 2006. The satirical series "looked back" on events of the first 30 years of the 21st century from the perspective of a nostalgia show in the year 2031 ...

Other sketches included were a look back on the program "Rape an Ape", the time Charlotte Church vomited herself inside out, and ...

The controversial third episode, which featured a mock look-back at a jumbo jet crashing into the British Houses of Parliament and an assassinated Tony Blair, was due to be screened on 17 August 2006, but was canceled in the wake of security threats in London airports and substituted by another episode. The canceled episode was subsequently shown a week later, without the footage of an assassinated Blair.

Clips are linked here, but I recommend viewing them through the Flash application.

Adam Buxton explains the "no news" clip:

For the time being here’s a compilation of a few bits along the theme of ‘No News’ that I did for Time Trumpet last year. People tend to think that it’s all footage I’ve got from the BBC of newsreaders before they go on air (which I did have access to), but I made these from transmitted footage, which I tinkered with to make it look as if they weren’t saying anything. It’s not funny as such but it’s pleasingly odd I think. Enjoy!