"Terrible Response to calls to change appointment"

I received a letter last week for an appointment this week which clashed with another appointment at the same hospital. I tried to contact them to re arrange this but despite spending hours and days trying the line it always ends up with a voice saying they are experiencing an abnormal amount of telephone calls and then the line goes dead.

I will probably end up wasting their and my time by not attending or getting their early and ask them to hurry up so I can attend my other appointment.

Why cannot they look at other appointments I have to ensure they don't clash. They all use the same system to make appointments.

Going through e-referrals doesn't work as it is not a referral but an annual equipment check.