I don't think the CAA will give out exam results over the phone
True. No point calling them as they won't tell you. We operate a prehistoric system here and the only ways I know are:
1. Wait for the CAA to post them to you - you'll get them roughly 2.5 weeks after your exams
2. Call your school. They can usually give you the results by phone once they have received them from the CAA - that also takes around 2 weeks after the exams.
DS