Finding an NHS dentist is nearly impossible in most of the UK, though.
I know that does not help someone who has become homeless or lost their job and cannot afford the 25 pounds a month (300 pounds a year). That is why I say it is important for people who are employed to get a Bupa insurance plan. Most people do that anyway. This reduces the burden on the NHS Dental and help provide free dental treatment for people who genuinely need it.
For non-dental medical issues, I think the NHS is pretty good. When I lived in UK, I always got same-day appointments for routine check-ups and same-week appointments for more complex investigations.
Furthermore, I would say that it's wrong to look at the situation in terms of "reducing the burden on the NHS Dental", since that is literally what's there for. If people don't opt for cosmetic surgery, then it's a healthcare issue and we created this institution/branch for this very purpose. Otherwise we can easily end up speaking in terms of how much of a burden being alive is, and how eating (regular) food and drinking water are poor economic decisions, a topsy-turvy way of looking at the very reason to have an 'economy'.
Respectfully that is completely wrong, do you even live here? Nobody wants to pay for private healthcare here (takeup is ~10%) and people don't care about teeth as much as they probably should.