Just a small update on what I've been researching...
It appears that the issue (on my part at least) may not solely be with DirectX 11 but instead my Nvidia driver as well. Nvidia has a chequered history with driver updates in that older games (3-5 years) lose their support with the more current software updates. The results are often seen through conflicts with DirectX which can materialise as texture or shading glitches. However, this doesn't change the fact that DA2 itself was never properlly configured with DirectX 11, with numerous graphical bugs having nothing to do with drivers at all.
Currently the driver version I use is 335.25 whilst the last confirmed working Nvidia driver for DA2 being 270.61 (Source: http://social.bioware.com/page/da2-patches). As you can see, there has been quite a few updates since then with ample time for DA2 to fall through the cracks of Nvidia's update roll out.
So how can you fix it?
As far as I can tell there are 3 methods:
1. Run the game on good ol' DirectX 9 - If you can stomach the noticable loss in graphical detail this would be the go to for you.
2. Return your Nvidia driver to the 270.61 build
3. Modding and replacing the current textures may in turn stop their conflict with both drivers. Download Aegrus's "Dragon Age 2 Ultimate HD" or trufflesduval's "Texture Mod" to completely retexture the majority of evironments. Both mods can be run in DirectX9 or 11 with little difference and have proven to almost remove the shading issues.
I hope this information helps and I will continue to find a more permanent solution.
Another issue which seems almost identical to this one can be found on the forums as well:
http://answers.ea.com/t5/Dragon-Age-2/Graphic-Glitches/m-p/2453134#U2453134