"Ineffective appointments processes"

I have a suspicious growth on my back and have been referred by my GP twice to have it checked out. I tried six times this afternoon to book my appointment however the telephone number provided on the letter has been busy each time. There is no answering service, email or alternative numbers. The letter says I have only have one week from the date of sending. This time window has been reduced by the weekend and a day in the post, effectively giving only 4 days. I have been referred by my GP for a second time as she is concerned about the growth, and if it is malignant time will be critical to ensuring a good outcome. The letter says this system is to give patients more choice about the date and time, but instead it seems to be an effective way to reduce waiting lists by denying patients to an appointment by having a continually engaged line, a limited time window to contact the line, and offering no alternative means of contact. To be clear, I will rearrange things to attend the soonest available appointment.