I didn't mention Have I Got News For You simply because I don't find it as funny, and it's the same with Buzzcocks. The difference being that I think, in general, Buzzcocks is amusing, but can be hit and miss. It's suffering without Amstel, tbh.
One of the most disappointing things for me, possibly ever, was seeing 'That Mitchell and Webb Look'. While I'm aware that Peep Show wasn't written by them, it almost
could've been, i.e the scripting suits David Mitchell and Robert Webb's characters to a tee, even to that point that they seem to have captured their real life personalities well. I'd love to see the writers of Peep Show creating more similar stuff. The aforementioned sketch show is woeful, except literally a handful of one-off sketches that were fairly amusing, and that pretty much summarises most British sketch shows, except the majority don't even have the funny scenes.
You can't argue with his ability, or the effect The Office has had on tv, I just feel it's helped influence a lot of things to be like it. As an example, I use things like 30 Rock and, obviously, The American Office, both of which are very similar, and neither of which I find particularly fantastic. True, but people like Chris Moyles don't really get 'undeserved hype', other than (perhaps) that he's seen as some sort of 'celebrity' and it doesn't influence much as a result. Gervais' hype on the other hand influences people to go out and watch things like The Invention of Lying, which isn't a good thing, imo.
I've read both O'Brian and Boyle's books, and Boyle's was immense. I get what you're saying, but Boyle's 'break' was through Mock the Week. Russell Howard is in a similar position, although I don't even find him slightly amusing. Because of this, their Mock the Week material is what they tend to use and recycle. Boyle has a lot of original stand-up material as well, but if you're an avid watcher of MTW, it's hard to tell which jokes are written for his stand-up circuits and which were for the panel show.