But I can't seem to get the backdrop to look right, when it's completely black she looks like she's floating etc.
At the minute I have one area light affecting the walls and the woman. The diamonds have there own light that I set up using a different tutorial, they're not really a problem except they could sparkle more!
Using Mental Ray, Ray tracing is on etc. Don't know what I'm doing wrong.
The Film Noir style you are trying to achieve will require a completely different lighting setup. The two area lights need to be removed and specific lights providing Key, Fill and highlights, and background lighting. Then specific lights need to be applied to the diamonds only.
To better achieve this, use mental ray materials instead of Maya shaders. And render in Mentalray.
Can you provide a zip files of all your textures and I can help set this up if you wish.