I don't have a GP. If I'm ill, I just go to a walk-in clinic. I can also schedule appointments online. When I was too sick to go out at all and due to a particular situation I didn't have web access either, I asked a neighbour to make a phone call for me. I live in a city where I can rely on the help of others.
For some official business, I use the landline at work to talk to banks or government. Most of the time I can use the web, though.
It is not a requirement for me to have a personal phone.