The way that it should work is by way of a DefaultValue create script in the comm_projectid field on the new communication screen.  If that's not there then you need to put it back in again.

There is no script on the field - I have created a new entity and no script is put on it the field in Communications.

Interestingly though if I go to New - New Appointment the field populates with the custom entity. But if I go to the communications tab of my custom entity and click the button 'New Appointment' then it doesn't populate. 

That suggests that those two actions go to different screens.  One correctly has the script in and the other one doesn't.

Which isn't the case as it's the standard communication screen (e.g. 'New Appointment' - CustomCommunicationDetailsBox)

Playing with it more I have found the problem, just don't know how to correct it. If I'm looking at the summary page of the Custom Entity and do 'New - New Appointment' then it works. But if go to the communication tab of the custom entity and do the same thing 'New - New Appointment' then it doesn't. It's like CRM has forgotten its 'Context' info when looking at the Communication tab (and the reason why the new task / appointment buttons don't work correctly) 

Which isn't the case as it's the standard communication screen (e.g. 'New Appointment' - CustomCommunicationDetailsBox)

Playing with it more I have found the problem, just don't know how to correct it. If I'm looking at the summary page of the Custom Entity and do 'New - New Appointment' then it works. But if go to the communication tab of the custom entity and do the same thing 'New - New Appointment' then it doesn't. It's like CRM has forgotten its 'Context' info when looking at the Communication tab (and the reason why the new task / appointment buttons don't work correctly) 

All solved, it's down to the ASP page. I have recreated the custom entity using the latest Entity Wizard (I'm using CRM and previously used the 2019 Entity Wizard, now using the 2021 as there isn't one for 2020) and this has corrected the issue.