Yeah, it can be tricky to find an NHS dentist that is taking patients... dentists in some areas of the country have waiting lists of over 2 years just to register!
Because of this, I've stayed registered with my childhood NHS dentist for my entire life, even though I now live in another part of the country, because I don't want to risk not being able to register somewhere else. In fact, just looking it up now: there are 16 dentists within 5 miles of where I live now, but only 1 of them is taking new NHS patients. In comparison, there are 4 dentists within 5 miles of where I grew up and 2 of them are taking new NHS patients.