The server was trying to pull its updates from WSUS, which was obviously failing. In order to get around this, you need to change the Registry:
Open Regedit and go to the following location:
HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\WindowsUpdate\AU
I found that I needed to create the WindowsUpdate then the AU key as they didn't exist.
Create a new DWORD called UseWUServer
Reboot the server and then you should be able to install the relevant features.