Appointments seem to depend on the basis of need.
My Surgery operate a forward appointment system for routine matters. Urgent appoinments, normally same day, are available if one phones or calls after 8.30 am. House calls are also possible.
If matters are really desperate then dial 999 for an Ambulance.
Can't be simpler than that. Most Surgeries operate the same way.
Also one can use Spire at Abergele if you don't mind coughing up in the monetry sense!