Finally, I have stumbled on to a bit of luck.
I like many others wanted a shirt that matched the screen caps.
On the dw_cosplay forum someone has already been asking about the shirt worn in The Girl in the Fireplace.
We've been told that it was probably the navy blue shirt, either: 'HIJKLMUVWXYZ', or a 'Reiss' dark blue cotton shirt.
Today I got lucky. I was going to pop into Banana Republic to grab some shirts for work. By chance I thought I would look at their clearance section. There was a single blue-green shirt, size Large. I inspected it and bought it 35% off the ticket price.
As far as I am concerned, it is perfect.
And now some color comparisons:
Here is the shirt in question. Of course the lighting for Tennant's run as the Doctor has played many a trick on our eyes when it comes to color matching.
On the far left is a slate grey shirt, like the H&M shirt that is worn in Tooth and Claw. The second from the left is my navy blue Banana Republic shirt, the third from the left is the "Slate Blue" Banana Republic bought from eBay and hand stitched by me. The last in the set is the blue/green shirt I will now be using as the Girl in the Fireplace shirt.
I didn't realize how popular a find this was going to be!
For those of you hunting for it I took some pictures:
From what I can tell the SKU: number is
The shirt itself a "slim fit" 16-16.5 Large,
Good luck if you're looking for it!