The NHS covers dental care for free, but only for young people, some students, people over 65, and those receiving benefits. As someone on a visa, you likely aren’t eligible for the free NHS services. But, you can choose the NHS flat fee for certain procedures, like fillings, crowns, and root canals.
UK dental service is a bit different than in the US. When you find a dentist and book an appointment, you’re booking an exam. The hygienist, which in my experience is always part of the deal with a US dental appointment, is a separate visit and cost. Without any NHS cover, a check-up can cost £30 (including a couple of x-rays), and a hygienist visit can cost over £70.
In my case, I also needed a root canal early in my time here. I could have paid £60 for NHS care, which would have been delayed and likely used adequate but old technology. I instead chose to pay a bunch more to go to a private dentist. Yes, just like in the US, people who have access to money are always going to be okay, but at least here, if you don’t have a few hundred pounds to spare, you can still get your dental health needs met.