Finally! I get to be the one to post something here instead of reading through everyone else's amazing discoveries!
Now, like most things, I can't 100% confirm I'm right. However, I think I've ID'd the exact monitor used from Series 3 onwards.
To the best of my knowledge it's a Samsung Syncmaster 193V N,
19" monitor.
I've attached some photos of it and some reference pics to show why I think this.
The main thing to look at is the sticker on the back of the monitor where you can make out the Samsung logo (just about), as well as the rest of the legal stuff. This photo is from the DW experience days. During the its use on the show, it seems this label was covered by some mechanical gizmo - which is where you can see the adhesive black marks covering parts of the sticker.
Trawling through reference photos, it would seem to be the same monitor used from Series 3 onwards, albeit with a variety of greebling and mounting changes. This doesn't look like the monitor used in Series 1 and 2 - although I will keep an eye out. Who knows, maybe I'll get lucky!
Now it is possible I'm only on the right track, and this isn't quite THE monitor. There is the 913BS, or the 192N, or who knows what else, which are possible contenders. Also, there is a 17" version of this monitor, but I've discounted it because it's label doesn't match as well and I'm fairly sure the TARDIS one was 19". Again, could be wrong there too.
I'd be more than thrilled to have someone challenge this and give an alternative monitor some love (mainly because I'd love to own one!), but I'm quite happy with this for now at least.
Thanks,
Matt