They only accept phone appointments for the day you call and every time I call they are fully booked so have to try again the following day - with the same response. 
 
Does your health centre/surgery have an online service?. If so, that is where I'd be trying next.  
It may be the case that if you phone, you can only make a (phone) appointment for that day. But you may be able to make a phone appointment for a later date by using their online 'e-consult'.  
My wife and I have both successfully used this service for our local health centre a few times since covid started.  
                            
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