"Impossible to book a blood test appointment over..."

I have been trying for 3 days now, very persistently - every 5-10 minutes - to book an appointment. Every single time, my call is diverted straight to voicemail and I am informed that due to the high volume of calls my call will be disconnected. I managed to find a number for the operator online. The lady who answered could not put me through either. She informed me that this was a problem that resulted from the type of queueing system used and has been reported numerous times but to no avail. She advised me to go to the hospital in person to make the appointment! She also gave a a number to call and complain. Guess what! When I called that number, my call went, once again, straight to voicemail and I was informed that this mailbox was full! To sum up, you cannot book an appointment over the phone and you cannot complain or speak to anyone in charge. You need to go to the hospital in person! In which day, age and country is this taking place?! I work full time and my employer was not impressed with my persistent phone attempts. But what choice do I have? Does anyone account for how much wasted time and resources this 'queueing system' costs the taxpayers? The same ones who actually pay for it? Incredible!