"Impossible to get an appointment"

I am a working woman in my 50s that needs to get a mirena coil removed that was put in under anaesthetic for medical reasons at Lewisham hospital, that has now been in far too long. I was told by my GP that I can only now have it removed at Waldron Sexual Health clinic. I have tried dialling on the dot at 10am a few times for an appointment - the phone system is a ridiculous lottery with no queuing system. For example I redialled about 30 times this morning to finally get through to a person (rather than an answer message) at 10.10 to be told all appointments were gone. I asked if I should come down to the walk-in as an alternative, and she said that all walk-in slots for the day were also gone - at 10.10 when the "walk-in" is supposedly open until 4. How is this a "walk-in" service? She said you need to actually arrive at 8.30 in the morning to be given a "slot" which might be later in the day and which you then have to go away and come back later. So basically you need to take a day off work on the "off-chance" you might get a slot.

The service is ridiculous and I'm now worried how I can ever get this mirena removed. Why is there not an alternative service eg via GPs to get a mirena removed for medical reasons that can actually be booked? Men do not have to go through such a ridiculous system to have a medical problem dealt with.