Not quite sure what you mean by accept your colour profile ?

I use Photobox on line printers and have always been happy.  They accept sRGB Jpeg images.

You could go to Peak Imaging if you want to upload Tiff I am not sure what printers they use and if they are able to supply a profile for it. Or there are smaller print shops who will supply a profile for their printers and accept aRGB if that is what you are looking for. Personally I wouldn't consider it unless there was a specific need.

sRGB Jpeg will show the image well enough for most people and certainly as good if not better than what you are looking at on the web. If you can see the detail here then you should see the detail in print !

And every one said, 'If we only live,
We too will go to sea in a Sieve,---
To the hills of the Chankly Bore!'
Far and few, far and few, Are the lands where the Jumblies live;
Their heads are green, and their hands are blue, And they went to sea in a Sieve.

Edward Lear
http://www.nonsenselit.org/Lear/ns/jumblies.html