Hi @bondoggie I haven't heard of anyone not being allowed to transfer our before. Check that you gave O2 the correct PAC (which should consist of 3 letters followed by 6 digits).
Otherwise you can try asking an agent to investigate using this form https://support2.giffgaff.com/app/ask/Number-transfers/Transferring-my-number-to-another-network/form/
Agents reply within 4 hours in the majority of cases but can take up to 24 hours, in the worst case, to reply (but they do work 7 days a week from 8am to 11pm). You will see when an agent has replied in the "Messages: From Agents" box which is half way down the right hand side of your "My Giffgaff" page or go here https://giffgaff.com/support/questions
NOTE that it is the network your transfer to that drives the number transfer process. The fact that giffgaff doesn't have a call centre is irrelevant as the process is mostly automated.