hi lou 26 sorry to hear you are in so much pain. Sounds as though you have what dentists might call peri-apical periodontitis associated with a non-vital tooth AKA an abscess.
I appreciate that it must be a major inconvenience not being able to walk on off the street into your dentist (incidentally you can't really do that at a doctors either, for fairly obvious reasons).
But have a think, you ring the dentist tommorow for a check-up appointment andf the receptionist will probably have an appointment in say 2 weeks, in some cases 3,4 5 etc..
Well if you have to wait X weeks for an appointment because the dentist/s are fully booked how do you expect to be able to ring up on a friday and walk in.
The obvious argument would be to have emergency only slots (I believe most dentists do) but if they are full, really what do you expect them to do.
If you went to A&E off the street you might wait upwards of 4 hours (although the staff get rather upset if you breach this time, government targets etc...)
Incidentally if you ever have an acute facial swelling and a dentist can't see you the only advice would be to attend A&E and perhaps asked to be seen by the SHO in oral and maxillofacial suregry