I'm no expert on the physics of sound, but AIUI sound is reflected off hard surfaces, especially boxy glass studios such as these the BBC are using. I think it's a case in point that sometimes it's best to stick to a proper, purpose-built studio. It may well look good but it certainly doesn't sound good. It always seems in modern broadcasting that most attention is given to how programmes look, but very little is paid to how they sound. Even in music terms, broadcasters are more than happy to spend thousands on snazzy titles and graphics, but then use cheaply made computerised news themes rather than paying for a real orchestra with real instruments which would sound infinitely better (as in years gone by). Anyway, just a pet hate of mine
It's not normally the surfaces behind the presenter which is the issue, as opposed to what's on the other side of the studio where they're facing, after all, they're talking forwards. A normal trick to help with lighting and sound is to tilt the windows at an angle, normally so the top is further out than the bottom, so that sound and lights are bounced back into the ceiling (which can then have some cheap sound treatment applied) as opposed to back into the mic / cameras.
One of the best things to absorb sound is people, often surprisingly so. Sadly you can't rely on them being quiet, so adding a studio audience to the Ten isn't such a good idea
I have to say though that watching the bits with Tim earlier, it didn't seem half as much of a problem as Fiona was having. Maybe Tim's more used to working on location and talking just that bit much louder that his mic can be faded down a bit so we don't hear the background noise and reflections.