A new update from Google is effecting the following:
The result is that Google Calendar will now only automatically add meetings to an invitee's calendar if the sender has previously interacted with them in Gmail.
SOLUTION:
If your invitees use Google Calendar and you haven't had any previous email interactions with them, they need to click 'I know the sender' and 'Yes' to accept your invitation.
There are some other things that can be done to improve this.
Your bookers can go to their Google calendar settings here and change the setting for "Add invitations to my calendar" from "Only if the sender is known" to "Everyone".