"Can’t get appt"

I have received a letter to set up an appt but have found it impossible to do so. By daytime telephone and online no appointments are available for the entirety of the bookable period (which I think is a month) and it’s impossible to book after that period. For example using the online service not a single appt is offered between today 15 September and the end of the bookable period, 22 October. They leave the option of phoning in a queue of 50 people at 0800 to see if an appt can be made that way, but that method is a complete waste of time, inefficient, and really no necessary for non urgent appts such as the one I am trying to arrange. I am increasingly using private online GP services for simple stuff but have no choice in respect of the particular letter I have received.