XBox One Controller Not Working After Anniversary Update

I've just applied the Windows 10 anniversary update and found my XBox One controller no longer worked. The controller appeared to switch on, but would then almost immediately switch itself off.

To solve this:

Remove the batteries from the controller.
Connect the controller to your PC via a USB cable.
Windows will install some device drivers.
My PC required a reboot to finish installation.
Re-insert batteries into the controller and disconnect USB cable.
Everything should now be back to normal.

Hope this helps!