So after a lot of Googling it appears I'm not alone in this issue.
The issue for you guys not getting a display is a handshaking problem between your GPU and monitor. The only resolution supported by UEFI is 1280X1024. If for some reason your GPU and TV/monitor don't handshake at that resolution, you'll see the splash screen but either get a garbled display or no display in UEFI. You'll also find you're fine when in Windows (for obvious reasons).
There is no fix for this from our side. The GPU VBIOS and monitor native resolution are where the problem lies. If the display you've connected does not handshake correctly with the GPU for whatever reason, it will likely default to its native resolution, and if that's anything other than 1280X1024 you've got a problem displaying UEFI. This happens with some TVs, projectors and monitors with certain GPUs. Older displays are more likely candidates for such problems, as are very high res monitors that use new conections ( DP 1.2 daisy chaining two monitors can create problems) . I suspect a VBIOS update from the GPU vendor might help, but chances of GPU vendors making specific VBIOS versions for this are unlikely. Only workaround is to connect a display that allows you to see UEFI or try using another method of connecting the GPU to the display (DVI instead of HDMI for example). Obviously, the latter is not a guaranteed workaround, as it depends how the display and GPU handshake on that output, too.
Problem seems to have appeared only after the 2nd last Nvidia driver update and the latest one didn't resolve it. So now if I want to enter the BIOS I've gotta plug the PC into the wee man's Xbox One S TV. Its not ideal but perfectly manageable.
