It can definitely be a long wait, especially if there's a shortage in the area. My fiance broke a tooth about 11 months ago. It took 3 months to get even an 'emergency' appointment by adding himself to the cancellation list. (Of course, when his mother phoned and they asked if he was in pain, she told them no.) All they did at that appointment was poke around for a few minutes, determine that nothing was infected or anything dire, and put him on the list for a follow-up appointment. Which he finally had last week. Where they still didn't fix anything, they just spent a little longer (10-15 minutes) making an assessment/treatment plan for his next appointment. Still don't know when that will be.
The wait to see the hygienist for a cleaning is going to be even longer, though once he's on that schedule, they're apparently pretty good about getting people in every 6 months.
To be fair, there's only the one dentist in the area, and he covers at least one other office, and there's only on hygienist working, so they've been building a backlog for some time. There also aren't really any other options (i.e. private dentists), so everyone is stuck waiting. Also, on the plus side, it being Scotland and him qualifying under the means testing, he'll get all this work done at no out-of-pocket cost. In the U.S., the work he'll need to have done would easily be over $1,000.