Well everything is on the same network and IP range, and I can ping every machine from any other machine - but, when I added a couple of workstations' IPs to the host file on the server it worked!
So it looks like unless I can find another way round it I've got to add ALL the workstations into the server's host file, and make sure any new machines also get added! What a bore - but it least it works.
Thanks for your help, kshah58!