I'm happy to report I kept on trying the chat service and it eventually worked and the PAC is being processed.
To help @Alyse and others, I was given the steps below, so try this if you haven't already, and if no good keep trying the chat service.
I also wasn't registered for My ID which you need to do first (I incorrectly assumed I was already registered when I ordered the SIM). Do this at https://my.idmobile.co.uk/web/cpw/pre-registration/-/registration/registerMyAccount
Once registered and logged in on my.idmobile.co.uk or the iD Mobile app...
1. Select 'Services' from the bottom menu in the app, or ‘My Services’ on the left-hand side on My Account.
2. Select ’Keep My Number’ in blue writing.
3. Type in the mobile number you want to keep.
4. Type in the PAC given to you by your previous network provider (3 letters, 6 digits).
5. Check that the information entered is correct.
6. Once you submit the information, we'll process your request.
Your number will be transferred on the next working day if you submit the request before 5pm.
If you submit it after 5pm, it will take 2 working days.