Hi pormerod,
It does sound like something on your work/school's network that is preventing Apple Configurator to function properly. The first two things I would check are your web filter and your firewall ports.
There are some ports that need to be opened for iPads to work with Apple's server if you are behind a firewall. Here is a list of known TCP and UDP ports used by Apple software products: http://support.apple.com/kb/HT6175?viewlocale=en_US
To use iPads behind a firewall (Configurator or not), you'll want to definitely open 5223 for Apple Push Notification and the standard ports for HTTP/HTTPS (80 and 443). If you're using an MDM, you will likely need to open 2195 and 2196 as well. If you still have issues port watch and see what an iPad does when trying to get to the store.
Check your web filter to see if any of Apple's servers are being blocked (software servers, activation servers, etc). Also some organizations will put a DNS block on Apple's update servers to prevent iOS devices from seeing or installing updates.
Chat with your network team to see if they can look at these things to help you identify the cause of the issues you are experiencing. Hope this helps!
~Joe