OK so the game arrived today and I installed it in Crossover Games 9.2
I initially got an error from the installer asking me to insert the original disc - the copy I purchased was still shrink-wrapped so I assumed this was a problem WINE was having with the copy protection. I tried copying the DVD contents to a hard disk (I'd been advised trying that previously for F.E.A.R & it fixed the problem in that case) but unfortunately with TR Underworld the same symptom was present from the hard disk. I decided to generate a log to see what was going on and when running the installer this way with the log enabled the installer worked fine :)
I then installed the 1.1 patch and ran the setup program. It auto detected my monitors native 1680x1050 and I changed the filtering to 8x Anisotropic from the default trilinear that it picked and switched on triple buffering. The game then loaded fine but the menu bar and dock remained visible - I'll submit a screenshot to Codeweavers.
Starting a new game Lara was orange with orange flares coming off her model. Most of the surrounding graphics were however fine and the game itself appeared to be working OK with the exception of the occasional pause for around a second (seemingly as it loads the next graphics so some buffering may be missing).
There are more reports of the game working on Linux with Wine versions from 1.1.3 to 1.3.5 but they all need a patch to prevent these graphics glitches (I didn't have any issues with audio that some had seen).