Ha. It works now I've replaced the Bluetooth adapator. So, pro-tip. If you want to use the Microsoft Surface Ergnomic keyboard with your desktop under Windows 10 I would suggest that you use the Pluggable Bluetooth USB adaptor. This works a treat. If you've got a Surface Pro 3 I'd advise you not to get this keyboard at all, or at least try it to make sure it works before you part with any cash.
I'm hammering away at the keyboard now and I like it very, very, much. My previous keyboard, the Microsoft Sculpt Comfort one, was very good but it lacked the numeric keyboard and arrow keys that I'm used to. Mine version of the Sculpt Comfort also has the American keyboard layout which works fine most of the time, but had me keeping an old keyboard around (really) just so I could type the backslash character. Which I can type just like this now: \\\\ Yay.