Apologies for the delayed reply due to the festive break. I raised it with Esri UK support who said much the same. From subsequent classes it does seem to be a local network inadequacy, as a couple of students running their own laptops at the same time, using the wireless network, saw no slowdown. Only those using lab desktop machines on the wired network were affected.
I will pursue with our local IT, but I expect more questions from them about the typical traffic generated, which UK support have not answered. What I am not sure about is the traffic flow for running something like a buffer. I (naively) assumed it was something like: the command is sent from the local machine, the tool runs on a server somewhere using the input also held in the cloud, creates the output in the cloud and then that output is delivered back to the local user. In that situation the only network traffic is sending the command and receiving the output, which seems trivial (the layers are very simple), so I don't understand the slowdown. There must be more to it?
I'm happy to accept it's not an AGOL limitation, but it would still be useful to know if anyone else has experienced the same and seen it resolved through network infrastructure improvements.
