Dear LPG,

I have found that the best way to contact my GP is by telephone these days.  If I find myself in need of a doctor, as long as I am ready to telephone, and hang on, I usually am able to get through and arrange a telephone consultation.  This allows me to talk to my doctor who will assess if I need a home visit or consultation and  he is, as a rule, able to arrange an appointment if needed. 

So the answer is to be extremely patient, persuasive, and firm to succeed. This usually works for me though it is not ideal.

BH, Catford