"Endless waiting to talk to someone"

I am waiting for an appointment for an angiogram, which, I am told, will be done at The Duchy Hospital. That was 10 days ago. Still waiting. The problem is that I have to make an urgent trip away from Cornwall before the end of May and I need to tell someone what dates I can't manage. Can I get through to anyone? No. All lines to Cardiology have been busy for about an hour and a half. No way even to leave a message or a voicemail.