Access requirements when speaking to the doctor

I wasn't really sure where to post this question,  so mental health issues looks like the most appropriate one.

I have post-traumatic stress disorder, and I regularly have nightmares/flashbacks in the night that keep me awake. I often sleep something like 12am to 4am and then again 7am to 10am, and because of this I can't make commitments in the morning. I tried recently making a regular commitment at 10 a.m., and I had to cancel it because it interfered too much with my sleep, which causes me a whole load of extra difficulties with everyday functioning.

I'm finding that this is making it difficult for me to make an appointment with my GP at the moment. I've tried ringing the surgery a few times in the last week. By the time I ring all of the appointments with him for that day are generally gone and they tell me that it's not possible to book an appointment to speak to him on a different day in the afternoon. They tell me I must wake up at 8:30 to ring them and book an appointment for the same day. I've tried to explain to the person who answers me on the phone that it is a disabled access requirement for me that I need to be able to book an appointment with the GP, to speak to him in the afternoon on a different day. Today for example they told me that this is not possible, but that I could speak to a different GP tomorrow afternoon. I don't feel like this is a satisfactory solution.

It seems to me that the problem is that the secretary who I speak to on the phone is probably quite busy booking different appointments, that their computer system is likely to be set up in a way which doesn't allow for what I currently need, and that if I'm going to be able to find a resolution to this difficulty I probably need to speak to somebody else than just the person who first answers the phone to me. My evaluation on the situation is that I have some additional needs as a result of my disability, and I'm asking them to make reasonable adjustments as a result of this and so they should have to do that. Does someone with more knowledge about this than me agree with my evaluation? It would be great to have some advice about how I can most effectively communicate to someone at the surgery who will listen to what I need about this and make some changes for me.

I've had this same difficulty with the doctors surgery for quite a long time, and I feel really angry about it. I have been managing and healing from PTSD for two years now and almost all of the healthcare support I've had has been private. I waited 9 months to get an NHS appointment for psychotherapy a year ago, and after the end of the 9 months a similar scenario happened and in the end I wasn't able to access the NHS service and they took me off the waiting list. From my perspective, the way these different NHS appointment booking systems are set up discriminates against me on grounds of my disability, as a result of my mental health. I find it particularly ironic (and infuriating? humiliating?) that the local NHS mental health service can't accommodate for this.