In this area there is a list, available at pharmacies etc., of NHS dentists with availability on their lists. There are always a few, though the list changes every now and then as some surgeries get full and others have people leave. It's so important for children's teeth to be well cared for and, even if you have to go 10 miles for a check-up, it's not so bad for just twice a year.
I read, only this morning, that Sainsburys are going to have dental surgeries in some larger stores. They will be private but treatment will, actually, be less than you pay on the NHS (unless you are entitled to free treatment). I like the idea of going for a packet of chocolate biscuits and a quick filling.