The Windows 10 Fall Creators update had a shiny new feature: hit [Win+]; or [Win+.] and you get a popup appear that lets you enter emoji directly into pretty much any supporting text field, Word document or even your IDE.
However, for anyone without a US keyboard, it seemed that you were stuck... the keyboard shortcut was only enabled for the en-US keyboard layout, so it wouldn't work if your keyboard layout was set to UK or anything else.
However, with a little trickery from this site, I've managed to get it working for the UK keyboard layout, and presumably any other layout you might want to use.
First, find the correct culture code here: https://msdn.microsoft.com/en-gb/library/ee825488(v=cs.20).aspx
I wanted en-GB, which is 0x0809
Then, copy the registry keys for the Emoji keyboard from [HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Input\Settings\proc_1\loc_0409\im_1] to your own locale - in my case, [HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Input\Settings\proc_1\loc_0809\im_1]
For a UK keyboard, a reg file like this does the job: